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215 Cards in this Set
- Front
- Back
- 3rd side (hint)
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Amy (150 lbs) and Gwen (50 lbs) are standing on slippery ice and Amy pushes off Gwen. How many forces are acting on Amy during the push if we ignore any friction between the ice skates and the ice?
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3!
The forces include her weight acting down, Normal force acting up and the reaction force from Gwen |
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Amy (150 lbs) and Gwen (50 lbs) are standing on slippery ice and Amy pushes off Gwen. Is momentum conserved if we just consider the motion of Amy?
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No, there is no net force acting on Amy so momentum is not conserved
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Amy (150 lbs) and Gwen (50 lbs) are standing on slippery ice and Amy pushes off Gwen. Is momentum conserved if we just consider the motion of Amy and Gwen?
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Yes, momentum is conserved because the net force on Gwen and Amy is zero.
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Amy (150 lbs) and Gwen (50 lbs) are standing on slippery ice and push off each other. If Amy slides at 6m/s, what speed does Gwen have?
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18 m/s
The initial momentum is zero, so the momentum of Amy and Gwen must be equal and opposite. Since p = mv, then if Amy has 3 times more mass, we see that Gwen must have 3 times more speed |
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A cannon sits on a stationary railroad flatcar with a total mass of 1000 kg. When a 10-kg cannon ball is fired to the left at a speed of 50 m/s, what is the recoil speed of the flatcar?
a) 0m/s b) 0.5m/s to the right c) 1 m/s to the right d) 20 m/s to the right e) 50 m/s to the right |
b) 0.5 m/s to the right
Since the initial momentum of the system was zero, the final total momentum must also be zero. Thus, the final momenta of the cannon ball and the flatcar must be equal and opposite. Pcannonball = (10kg)(50m/s) = 500 kg-m/s Pflatcar = 500 kg-m/s = (1000 kg)(0.5 m/s) |
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In the game of tetherball, the struck ball whirls around a pole. In what direction does the net force on the ball point?
1) toward the top of the pole 2) toward the ground 3) along the horizontal component of the tension force 4) along the vertical component of the tension force 5) tangential to the circle |
3) along the horizonal component of the tension force
The vertical component of the tension balances the weight. The horizontal component of tension provides the centripetal force that points toward the center of the circle. |
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You are a passenger in a car, not wearing a seat belt. The car makes a sharp left turn. From your perspective, what do you feel is happening to you?
1) you are thrown to the right 2) you feel no particular change 3) you are thrown to the left 4) you are thrown to the ceiling 5) you are thrown to the floor |
1) you are thrown to the right
The passenger has the tendency to continue moving in a straight line. From your perspective in the car, it feels like you are being thrown to the right, hitting the passenger door |
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During that sharp left turn, you found yourself hitting the passenger door. What is the correct description of what is actually happening?
1) centrifugal force is pushing you into the door 2) the door is exerting a leftward force on you 3) both of the above 4) none of the above |
2) The door is exerting a leftward force on you
The passenger has the tendency to continue moving in a straight line. There is centripetal force, provided by the door, that forces the passenger into a circular path. |
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You drive your dad's car too fast around a curve and the car starts to skid. What is the correct description of this situation?
1) car's engine is not strong enough to keep the car from being pushed out 2) friction between tires and road is not strong enough to keep car in a circle 3) car is too heavy to make the turn 4) none of the above |
2) friction between tires and road is not strong enough to keep car in a circle
The friction force between tires and road provides the centripetal force that keeps the car moving in a circle. If this force is too small, the car continues in a straight line |
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Two equal-mass rocks tied to strings are whirled in horizontal circles. The radius of circle 2 is twice that of circle 1. If the period of motion is the same for both rocks, what is the tension in cord 2 compared to cord 1?
1) T2 = 1/4 T1 2) T2 = 1/2 T1 3) T2 = T1 4) T2 = 2 T1 5) T2 = 4 T1 |
4) T2 = 2 T1
The centripetal force in this case is given by the tension, so T = mv²2/r. For the same period, we find that v2 = 2v1 (and this term is squared). However, for the denominator, we see that r2 = 2 r1, which gives us the relation T2 = 2 T1 |
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You're on a Ferris wheel moving in a vertical circle. When the Ferris wheel is at rest, the normal force N exerted by your seat is equal to your weight mg. How does N change at the top of the Ferris wheel when you are in motion?
1) N remains equal to mg 2) N is smaller than mg 3) N is larger than mg 4) none of the above |
2) N is smaller than mg
You are in circular motion, so there has to be a centripetal force pointing inward. At the top, the only two forces are mg (down) and N (up), so N must be smaller than mg. |
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A skier goes over a small round hill with radius R. Since she is in circular motion, there has to be a centripetal force. At the top of the hill, what is Fc of the skier equal to?
1) Fc = N + mg 2) Fc = mg - N 3) Fc = T + N - mg 4) Fc = N 5) Fc = mg |
2) Fc = mg - N
Fc points toward the center of the circle, i.e. downward in this case. The weight vector points down and the normal force (exerted by the hill) points up. The magnitude of the net force, therefore, is: Fc = mg - N |
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You swing a ball at the end of a string in a vertical circle. Since the ball is in circular motion there has to be a centripetal force. At the top of the ball's path, what is Fc equal to?
1) Fc = T - mg 2) Fc = T + N - mg 3) Fc = T + mg 4) Fc = T 5) Fc = mg |
3) Fc = T + mg
Fc points toward the center of the circle, i.e. downward in this case. The weight vector points down and the tension (exerted by the string) also points down. The magnitude of the net force, therefore, is: Fc = T + mg |
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Which is stronger, Earth's pull on the Moon, or the Moon's pull on the Earth?
1) the Earth pulls harder on the Moon 2) the Moon pulls harder on the Earth 3) they pull on each other equally 4) there is no force between the Earth and the Moon 5) it depends upon where the Moon is in its orbit at that time |
3) they pull on each other equally
Newton's 3rd law |
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If the distance to the Moon were doubled, then the force of attraction between Earth and the Moon would be
1) one quarter 2) one half 3) the same 4) two times 5) four times |
1) one quarter
the gravitational force depends inversely on the distance squared. So if you increase the distance by a factor of 2, the force will decrease by a factor of 4. F = G Mm/r^2 |
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You weigh yourself on a scale inside an airplane that is flying with constant speed at an altitude of 20,000 feet. How does your measured weight in the airplane compare with your weight as measured on the surface of the Earth?
1) greater than 2) less than 3) same |
2) less than
At a high altitude, you are farther away from the center of the Earth. Therefore, the gravitational force in the airplane will be less than the force that you would experience on the surface of the Earth. |
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Two satellites A and B of the same mass are going around Earth in concentric orbits. The distance of satellite B from Earth's center is twice that of satellite A. What is the ratio of the centripetal force acting on B compared to that acting on A?
1) 1/8 2) 1/4 3) 1/2 4) it's the same 5) 2 |
2) 1/4
Using the law of Gravitation F = G Mm/r² (note the 1/r² factor) |
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The Moon does not crash into the Earth because:
1) it's in Earth's gravitational field 2) the net force on it is zero 3) it is beyond the main pull of Earth's gravity 4) it's being pulled by the Sun as well as by Earth 5) none of the above |
5) none of the above
The Moon does not crash into Earth because of its high speed. If it stopped moving, it would, of course, fall directly into Earth. With its high speed, the Moon would fly off into space if it weren't for gravity providing the centripetal force. |
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Astronauts in the space shuttle float because:
1) They are so far from Earth that Earth's gravity doesn't act any more 2) Gravity's force pulling them inward is cancelled by the centripetal force pushing them outward 3) While gravity is trying to pull them inward, they are trying to continue on a straight-line path 4) Their weight is reduced in space so the force of gravity is much weaker |
3) While gravity is trying to pull them inward, they are trying to continue on a straight-line path
Astronauts in the space shuttle float because they are in "free fall" around Earth, just like a satellite or the Moon. Again, it is gravity that provides the centripetal force that keeps them in circular motion. |
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If you weigh yourself at the equator of Earth, would you get a bigger, smaller, or similar value than if you weigh yourself at one of the poles?
1) bigger value 2) smaller value 3) same value |
2) smaller value
The weight that a scale reads is the normal force exerted by the floor (or the scale). At the equator, you are in circular motion, so there must be a net inward force toward Earth's center. This means that the normal force must be slightly less than mg. So the scale would register something less than your actual weight |
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You're on a Ferris wheel moving in a vertical circle. When the Ferris wheel is at rest, the normal force N exerted by your seat is equal to your weight mg. How does N change at the top of the Ferris wheel when you are in motion?
1) N remains equal to mg 2) N is smaller than mg 3) N is larger than mg 4) none of the above |
2) N is smaller than mg
You are in circular motion, so there has to be a centripetal force pointing inward. At the top, the only two forces are mg (down) and N (up), so N must be smaller than mg. |
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A skier goes over a small round hill with radius R. Since she is in circular motion, there has to be a centripetal force. At the top of the hill, what is Fc of the skier equal to?
1) Fc = N + mg 2) Fc = mg - N 3) Fc = T + N - mg 4) Fc = N 5) Fc = mg |
2) Fc = mg - N
Fc points toward the center of the circle, i.e. downward in this case. The weight vector points down and the normal force (exerted by the hill) points up. The magnitude of the net force, therefore, is: Fc = mg - N |
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You swing a ball at the end of a string in a vertical circle. Since the ball is in circular motion there has to be a centripetal force. At the top of the ball's path, what is Fc equal to?
1) Fc = T - mg 2) Fc = T + N - mg 3) Fc = T + mg 4) Fc = T 5) Fc = mg |
3) Fc = T + mg
Fc points toward the center of the circle, i.e. downward in this case. The weight vector points down and the tension (exerted by the string) also points down. The magnitude of the net force, therefore, is: Fc = T + mg |
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Which is stronger, Earth's pull on the Moon, or the Moon's pull on the Earth?
1) the Earth pulls harder on the Moon 2) the Moon pulls harder on the Earth 3) they pull on each other equally 4) there is no force between the Earth and the Moon 5) it depends upon where the Moon is in its orbit at that time |
3) they pull on each other equally
Newton's 3rd law |
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If the distance to the Moon were doubled, then the force of attraction between Earth and the Moon would be
1) one quarter 2) one half 3) the same 4) two times 5) four times |
1) one quarter
the gravitational force depends inversely on the distance squared. So if you increase the distance by a factor of 2, the force will decrease by a factor of 4. F = G Mm/r^2 |
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You weigh yourself on a scale inside an airplane that is flying with constant speed at an altitude of 20,000 feet. How does your measured weight in the airplane compare with your weight as measured on the surface of the Earth?
1) greater than 2) less than 3) same |
2) less than
At a high altitude, you are farther away from the center of the Earth. Therefore, the gravitational force in the airplane will be less than the force that you would experience on the surface of the Earth. |
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Two satellites A and B of the same mass are going around Earth in concentric orbits. The distance of satellite B from Earth's center is twice that of satellite A. What is the ratio of the centripetal force acting on B compared to that acting on A?
1) 1/8 2) 1/4 3) 1/2 4) it's the same 5) 2 |
2) 1/4
Using the law of Gravitation F = G M1m2/r^2 (note the 1/r^2 factor) |
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The Moon does not crash into the Earth because:
1) it's in Earth's gravitational field 2) the net force on it is zero 3) it is beyond the main pull of Earth's gravity 4) it's being pulled by the Sun as well as by Earth 5) none of the above |
5) none of the above
The Moon does not crash into Earth because of its high speed. If it stopped moving, it would, of course, fall directly into Earth. With its high speed, the Moon would fly off into space if it weren't for gravity providing the centripetal force. |
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Astronauts in the space shuttle float because:
1) They are so far from Earth that Earth's gravity doesn't act any more 2) Gravity's force pulling them inward is cancelled by the centripetal force pushing them outward 3) While gravity is trying to pull them inward, they are trying to continue on a straight-line path 4) Their weight is reduced in space so the force of gravity is much weaker |
3) While gravity is trying to pull them inward, they are trying to continue on a straight-line path
Astronauts in the space shuttle float because they are in "free fall" around Earth, just like a satellite or the Moon. Again, it is gravity that provides the centripetal force that keeps them in circular motion. |
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If you weigh yourself at the equator of Earth, would you get a bigger, smaller, or similar value than if you weigh yourself at one of the poles?
1) bigger value 2) smaller value 3) same value |
2) smaller value
The weight that a scale reads is the normal force exerted by the floor (or the scale). At the equator, you are in circular motion, so there must be a net inward force toward Earth's center. This means that the normal force must be slightly less than mg. So the scale would register something less than your actual weight |
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Work
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the product of the magnitude of the displacement times the component of the force parallel to the displacement
W = F * d where F is the component of constant force F parallel to the displacement d, also: W = Fd cos θ |
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If a person is walking with a heavy bag of groceries in their hands at a constant velocity, are they doing work on the bag?
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No
Because the displacement and force exerted on the bag are perpendicular to each other, not parallel |
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Would a hiker do the same amount of work on a backpack if he the climbed a hill with height of "h" if he lifted the backpack the same height of "h"?
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YES
work done depends only on the change in elevation and not on the angle of the hill. The hiker would do the same work to lift the pack vertically the same height "h" |
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A hiker wears a backpack and hikes up a hill:
Is work done on the pack? Does the hiker do work on the pack? Does gravity do work on the pack? |
No net work
Yes, the hiker does positive work on the pack Yes, gravity does negative work on the pack |
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Does the Earth do work on the Moon?
Does gravity do positive work, negative work, or no work? |
The gravitational force exerted by the Earth on the Moon acts towards the Earth and provides its centripetal acceleration, inward along the radius of the Moon's orbit. The Moon's displacement at any moment is tangent to the circle, in the direction of its velocity, perpendicular to the radius and perpendicular to the force of gravity. Hence the angle θ between the force Fg and the instantaneous displacement of the Moon is 90º, and the work done by the Earth's gravity on the moon as it orbits is therefore zero.
This is why the Moon, as well as artificial satellites, can stay in orbit without expenditure of fuel: no net work needs to be done against the force of gravity |
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Work done by a Variable Force
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The work done by a variable force of moving an object between two points is EQUAL to the area under the F vs d curve between those two points
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Conservation of Energy
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The sum of all types, the TOTAL ENERGY is the same after any process as it was before: that is the quantity ENERGY is conserved
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Energy
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the ability to do work
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Kinetic Energy
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Energy of motion
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Work-energy principle
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The net work done on an object is equal to the change in an objects kinetic energy
Wnet = ∆KE |
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Translational Kinetic Energy
(units) |
KE = 1/2mv^2
J = kg * (m/v)^2 |
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Potential Energy
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The energy associated with forces that depend on the position or configuration of an object relative to its surroundings
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Gravitational Potential Energy
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An object, due to Earth's gravity, as the product of the object's weight (mg) and its height (y) above some reference level (such as the ground)
PEgrav = mgy |
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The higher an object is above the ground, the more gravitational potential energy it has
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Wext = mg(y2 - y1)
Wext = PE2 - PE1 = ∆PE In terms of work done by gravity itself: Wg = -mg(y2 - y1) Wg = -(PE2 - PE1) = -∆PE |
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Work done by gravity
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The work done by gravity as the object of mass m moves from point 1 to point 2 is equal to the negative of the difference in potential energy between positions 1 and 2
Wg = -mg(y2 - y1) Wg = -(PE2 - PE1) = -∆PE |
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Spring equation/Hooke's Law
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Fs = -kx
This force is sometimes called a "restoring force" because the spring exerts its force in the direction opposite the displacement (hence the minus sign) The work done is then: W = Fx = 1/2kx² |
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Elastic Potential Energy
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elastic PE = 1/2kx²
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If a spring is COMPRESSED a distance "x" from its natural length, the average force is:
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F = 1/2kx
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Conservative Forces
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Forces such as gravity, for which the work done does not depend on the path taken but only on the initial and final positions
The elastic force of a spring (or other elastic material) in which F = -kx, is a conservative force |
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Nonconservative Force
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An example is friction since the work it does depends on the path. For example, when a crate is moved across the floor from one point to another, the work done depends on whether the path taken is straight or is curved
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Is potential energy conservative or nonconservative?
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Conservative
Because potential energy is energy associated with the position or configuration of objects, potential energy can only make sense if it can be stated uniquely for a given point |
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Work-energy principle
Conservative forces |
Wnet = Wc + Wnc
Then from the work-energy principle, we have: Wnet = ∆KE Wc + Wnc = ∆KE where ∆KE = KE2 - KE1 then Wnc = ∆KE - Wc { Wnc = ∆KE + ∆PE } |
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Principle of Conservation of Mechanical Energy
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If only conservative forces are acting, the total mechanical energy of a system neither increases nor decreases in any process. It stays constant--it is conserved
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SPEEDS ON TWO WATER SLIDES
Two water slides at a pool are shaped differently, but have the same length and start at the same height "h." Two riders Paul and Kathleen, start from rest at the same time on different slides. (a) Which rider is traveling faster at the bottom and (b) which rider makes it to the bottom first? |
(a) Each rider's initial potential energy "mgh" gets transformed to kinetic energy so the speed "v" at the bottom is obtained from 1/2mv² = mgh. The mass cancels and so the speed will be the same, regardless of the mass of the rider. SINCE THEY DESCEND THE SAME VERTICAL HEIGHT, THEY WILL FINISH WITH THE SAME SPEED.
(b) Note that Kathleen is consistently at a lower elevation than Paul at any instant, until the end. This means she has CONVERTED her POTENTIAL ENERGY to KINETIC ENERGY EARLIER. Consequently, she is traveling faster than Paul for the WHOLE trip, except toward the end where Paul finally gets up to the same speed, SInce she was going faster for the whole trip, and the distance is the same, Kathleen gets to the bottom first. |
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When is work done?
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Work is done when energy is transferred from one object to another
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Law of Conservation of Energy
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The total energy is neither increased nor decreased in any process. Energy can be transformed from one form to another, and transferred from one object to another, but the total amount remains constant.
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What force is called a Dissipative Force?
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Because friction forces reduce the total mechanical energy (but NOT the total energy), they are called dissipative forces
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Power
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the rate at which work is done
P = average power = work/time = energy transformed/time P = W/t = mgy/t = Fd/t = Fv units = W = J/s = (kg*m/s^2*m)/(s) |
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Uniform Circular Motion
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An object that moves in a circle at constant speed
*magnitude of the velocity remains the same but direction of the velocity continuously changes |
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Centripetal Acceleration
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An object moving in a circle of radius "r" at constant speed "v" has an acceleration whose direction is toward the center of the circle and whose magnitude is
aR = v^2/r It is not surprising that this acceleration depends on "v" and "r." The greater the speed, the faster the velocity changes direction; and the larger the radius, the less rapidly the velocity changes direction. |
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Velocity of an object moving in a circle
(Name that equation) |
v = 2πr/T
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What direction is the force and acceleration pointed for an object in circular motion?
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Both are directed toward the center of the circle. Velocity is always directed 90º from the force/acceleration.
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TETHERBALL
The game of tetherball is played with a ball tied to a pole with a string. After the ball is struck, it revolves around the pole. In what direction is the acceleration of the ball, and what force causes the acceleration? |
If the ball revolves in a horizontal plane as shown, then the acceleration points horizontally toward the center of the ball's circular path (not towards the top of the pole). The force responsible for the acceleration may not be obvious at first, since there seems to be no force pointing directly horizontally. But it is the net force (sum of Ftension and mg here) that must point in the direction of the acceleration. The vertical component of the string tension, Fty, balances the balls weight, mg. The horizontal component of the string tension, Ftx, is the force that produces the centripetal acceleration toward the center.
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Force required to give a vehicle its centripetal acceleration on a banked curve
(Name that equation!) |
FN sin θ = mv²/r
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BANKING ANGLE
For a car traveling with speed "v" around a curve of radius "r", determine a formula for the angle at which road should be banked so that no friction is required? |
tan θ = v²/rg
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Newton's Law of Universal Gravitation
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Every particle in the universe attracts every other particle with a force that is proportional to the product of their masses and inversely proportional to the square of the distance between them. This force acts along the line joining the two particles:
F = G(m₁m₂)/r² G = 6.67e-11 Nm²/kg² |
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Does the Earth exert more force on the Moon? Or does the moon exert more force on the earth?
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The gravitational force one object exerts on a second object is directed toward the first object, and (by Newton's third law) is equal and opposite to the force exerted by the second object on the first
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What keeps a satellite up?
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its high speed
If a satellite stopped moving, it would fall directly to Earth |
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Kepler's first law of planetary motion
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The path of each planet about the Sun is an ellipse with the Sun at one focus
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Kepler's second law of planetary motion
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Each planet moves so that an imaginary line drawn from the Sun to the planet sweeps out equal areas in equal periods of time
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Kepler's third law of planetary motion
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The ration of the squares of the periods "T" of any two planets revolving about the Sun is equal to the ratio of the cubes of their mean distances from the Sun
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Momentum
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the product of an object's mass times velocity
also a vector quantity |
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Newton's Second Law of Motion
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The rate of change of momentum of an object is equal to the net force applied to it.
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Law of Conservation of Momentum
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The total momentum of an isolated system of objects remains constant
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Isolated system
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One which only significant forces are those between the objects in the system. The sum of these forces within the system will be zero because of Newton's third law.
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External Forces
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Forces exerted by objects outside the system--and they don't add up to zero (vectorially), then the total momentum of the system won't be conserved
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A railroad car traveling at a speed "v" collides an identical car which is at rest. Is momentum conserved?
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We chose our system to be the two railroad cars. We have no external forces, so momentum is conserved
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FALLING ON OR OFF A SLED
An empty sled is sliding on frictionless ice when Susan drops vertically from a tree above onto the sled. . When she lands does the sled speed up, slow down, or keep the same speed? (b) Later, Susan falls sideways off the sled. When she drops off, does the sled speed up, slow down, or keep the same speed? |
(a) Because Susan falls vertically onto the sled, she has no initial horizontal momentum. Thus the total horizontal momentum afterwards equals the momentum of the sled initially. Since the mass of the system has increased, the speed must increase
(b) At the instant Susan falls off, she is moving with the same horizontal speed as she was while on the sled. At the moment she leaves the sled, she has the same momentum she had an instant before. Because momentum is conserved, the sled keeps the same speed. |
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Center of Mass
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The sum of the translational motion of the CM, plus rotational, vibrational, or other types of motion about the CM
Xcm = (Xa + Xb)/2 |
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Center of Gravity
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A similar concept to center of mass; the force of gravity actually acts on all the different parts of an object. There is a conceptual difference between the center of gravity and center of mass, but for nearly all practical purposes, they are at the same point
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A TWO STAGE ROCKET
A rocket is shot into the air. At the moment the rocket reaches its highest point, a horizontal distance d from its starting point, a prearranged explosion separates it into two parts of equal mass. Part I is stopped in midair by the explosion, and it falls vertically to Earth. Where does part II land? |
After the rocket is fired, the path of the CM of the system continues to follow the parabolic trajectory of a projectile acted on by only a constant gravitational force. The CM will thus land at a point 2d from the starting point. Since the massed of I and II are equal, the CM must be midway between them at any time. Therefore, part II lands 3d from the starting point
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Phases of matter
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solid, liquid, gas
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Fluids
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since liquids and gases do not maintain a fixed shape they both have the ability to flow
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Density
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an objects mass per unit volume
ρ = m/v |
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Specific Gravity
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The density of a substance to the density of water
because specific gravity is a ration, it is a simple number without dimensions or units |
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Pressure
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Force per unit area, where the force F is understood to be the magnitude of the force acting perpendicular to the surface area A:
pressure = P = F/A *units are pascals |
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Pressure in fluids
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A fluid can exert a pressure in any direction
pressure is the same in every direction in a fluid at a given depth; if it weren't, the fluid would be in motion |
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Gauge Pressure/Absolute Pressure
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Note a tire registers the pressure above and beyond atmospheric pressure. Thus we must add the atmospheric pressure,
P = PA + PG |
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1 Atmosphere
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The pressure of the air at a given place varies slightly according to the weather. At sea level, the pressure of the atmosphere on average is:
1.013 × 10⁵ N/m² = 101300 Pascals |
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Pascal's Principle
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If an external pressure is applied to a confined fluid, the pressure at every point within the fluid increases by that amount
Pout = Pin |
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SUCTION
You sit in a meeting where a novice NASA engineer proposes suction cup shoes for Space Shuttle astronauts working on the exterior of the spacecraft. What is the fallacy of this plan? |
Suction cups work by pushing out the air underneath the cup. What hold the cup in place is the air pressure outside the cup but in outer space, there is no air pressure to hold the suction cup onto the aircraft
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Sucking Through a Straw
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We sometimes mistakenly think of suction as something we actively do. For example, we intuitively think that we pull the soda up through a straw. Instead what we do is lower the pressure at the top of the straw and the atmosphere pushes the soda up the straw
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Buoyant Force
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Fluid exerts an upward force on the bottom of objects partially and fully submerged. The net force exerted by the fluid pressure is the buoyant force and acts upward
FB = F₂ - F₁ = ρfgA(h₂-h₁) = ρfVg =mfg |
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Archimedes principle
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The buoyant force of on an object immersed in a fluid is equal to the weight of the fluid displaced by that object
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TWO PAILS OF WATER
Consider two identical pails of water filled to the brim. One pail contains only water, the other has a piece of wood floating in it. Which pail has the greater weight? What is the principle involved? |
Both pails weigh the same. Recall Archimedes' principle: the wood displaces a volume of water with weight equal to the weight of the wood. Some water will overflow the pail, but Archimedes' principle tells us the spilled water has weight equal to that of the wood; so the pails have the same weight
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Floating objects
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An object floats on a fluid if its density is less that that of the fluid
Vdisplaced/V₀ = ρ₀/ρf |
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Fluids in motion
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We can distinguish between two types of fluid flow: if the flow is smooth, such that neighboring layers of the fluid slide by each other smoothly, the flow is said to be streamline or laminar flow. In streamline flow, each particle of the fluid follows a smooth path, called a streamline, and these paths do not cross one another.
Above a certain speed, the flow becomes turbulent: characterized by erratic, small, whirlpool-like circles called "eddies." |
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Equation of Continuity
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ρ₁A₁v₁ = ρ₂A₂v₂
If no fluid flows in or out of the sides, the flow rates through A₁ and A₂ must be equal |
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Bernoulli's Principle
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Where the velocity of a fluid is high, the pressure is low, and where the velocity is low, the pressure is high.
Bernoulli's equation: W₁= F₁l₁ = P₁A₁Δl₁ At point 2, the work done on our cross section of fluid is W₂ = -P₂A₂Δl₂ W₃ = -mg(y₂-y₁) W = W₁ + W₂ + W when we rearrange we get: P₁ + ½ρv₁² + ρgy₁ = P₂ + ½ρ₂² + ρgy₂ |
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Airplane Wings and Dynamic Lift
State the principle involved |
Airplanes experience a "life" force on their wings, keeping them up in the air if they are moving at relatively high speed relative to the air and the wing is tilted upward at a small angle. Because the air speed is greater above the wing that below it, the pressure above the wing is less than the pressure below the wing (Bernoulli's principle). Hence the net upward force on the wing called dynamic lift
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Sailboats
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A sailboat can move against the wind with the aid of the Bernouilli effect, by setting the sails at an angle. The air travels rapidly over the bulging front surface of the sail, and the relatively still air behind the sail exerts a greater pressure resulting in a net force on the sail.
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Baseball Curve
State the Principle Involved |
Why a spinning baseball curves can be explained by Bernoulli's principle. Suppose the ball is rotating counter-clockwise as seen from above. A thin layer of air is being dragged around by the ball, and this layer tens to slow down the oncoming air. The air rotating with the ball adds to its speed so the speed is higher on one side of the ball than on the other. The higher speed on one side means that the pressure is lower on the side that is moving faster than the side that is moving slower. We see is interaction as the ball curving to one side
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Why does smoke go up a chimney?
State the Principle involved |
Its partly because hot air rises (it's less dense and therefore buoyant). But Bernoulli's principle also plays a role. When wind blows across the top of a chimney, the pressure is less there than inside the house. Hence, air and smoke are pushed up the chimney by the higher indoor pressure
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First Condition for Equilibrium
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For an object to be at rest, Newton's second law tells us that the sum of the forces must add up to zero. Since force is a vector, the components of the net force must each be zero
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Second Condition for Equilibrium
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The net torque applied to an object in equilibrium must be zero
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A LEVER
A bar is used to pry a large rock by being set in between the large rock and a smaller rock. The small rock acts as a fulcrum (pivot point). The force required at the long end of the bar is much smaller than the rocks weight. If, however, the leverage isn't sufficient, and the large rock is not budged, what are two ways to increase the leverage? |
By slipping a pipe over the end of the bar and thereby pushing with a longer lever arm. A second way is to move the fulcrum closer to the large rock. This may change the short lever arm only a little, but the long lever arm is significantly changed.
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If one material has a higher density than another, does this mean that the molecules of the first material must be more massive than those of the second?
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Yes
Since density is defined as ρ = M/V, the volume matters as well. Thus, it could be simply that the first material has a more compact arrangement of molecules, such that there are more molecules in a given volume, which would lead to a higher density. |
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Consider what happens when you push both a pin and the blunt end of a pen against your skin with the same force. What will determine whether your skin will be punctured?
1) the pressure on your skin 2) the net applied force on your skin 3) both pressure and net applied force are equivalent 4) neither pressure nor net applied force are relevant here |
1) the pressure on your skin
The net force is the same in both cases. However, in the case of the pin, that force is concentrated over a much smaller area of contact with the skin, such that the pressure is much greater. Since the force per unit area (i.e., pressure) is greater, the pin is more likely to puncture the skin for that reason. |
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You are walking out on a frozen lake and you begin to hear the ice cracking beneath you. What is your best strategy for getting off the ice safely?
1) stand absolutely still and don’t move a muscle 2) jump up and down to lessen your contact time with the ice 3) try to leap in one bound to the bank of the lake 4) shuffle your feet (without lifting them) to move towards shore 5) lie down flat on the ice and crawl toward shore |
5) lie down flat on the ice and crawl toward shore
As long as you are on the ice, your weight is pushing down. What is important is not the net force on the ice, but the force exerted on a given small area of ice (i.e., the pressure!). By lying down flat, you distribute your weight over the widest possible area, thus reducing the force per unit area. |
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While swimming near the bottom of a pool, you let out a small bubble of air. As the bubble rises toward the surface, what happens to its diameter?
1) bubble diameter decreases 2) bubble diameter stays the same 2)bubble diameter increases |
3) bubble diameter increases
As the bubble rises, its depth decreases, so the water pressure surrounding the bubble also decreases. This allows the air in the bubble to expand (due to the decreased pressure outside) and so the bubble diameter will increase. |
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Three containers are filled with water to the same height and have the same surface area at the base, but the total weight of water is different for each. Which container has the greatest total force acting on its base?
1) container 1 2) container 2 3) container 3 4) all three are equal |
4) All three are equal
The pressure at the bottom of each container depends only on the height of water above it! This is the same for all the containers. The total force is the product of the pressure times the area of the base, but since the base is also the same for all containers, the total force is the same. |
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When a hole is made in the side of a Coke can holding water, water flows out and follows a parabolic trajectory. If the container is dropped in free fall, the water flow will:
1) diminish 2) stop altogether 3) go out in a straight line 4) curve upwards |
2) stop altogether
Water flows out of the hole because the water pressure inside is larger than the air pressure outside. The water pressure is due to the weight of the water. When the can is in free fall, the water is weightless, so the water pressure is zero, and hence no water is pushed out of the hole! |
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When you drink liquid through a straw, which of the items listed below is primarily responsible for this to work?
1) water pressure 2) gravity 3) inertia 4) atmospheric pressure 5) mass |
4) Atmospheric pressure
When you suck on a straw, you expand your lungs, which reduces the air pressure inside your mouth to less than atmospheric pressure. Then the atmospheric pressure pushing on the liquid in the glass provides a net upward force on the liquid in the straw sufficient to push the liquid up the straw. |
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Imagine holding two identical bricks in place under water. Brick 1 is just beneath the surface of the water, while brick 2 is held about 2 feet down. The force needed to hold brick 2 in place is:
1) greater 2) the same 3) smaller |
2) the same
The force needed to hold the brick in place underwater is: W – FB. According to Archimedes’ Principle, FB is equal to the weight of the fluid displaced. Since each brick displaces the same amount of fluid, then FB is the same in both cases. |
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An aluminum cylinder and a pail together weigh 29 N, as read on a scale. With the cylinder submerged, the scale reads 20 N. If the displaced water is poured into the pail, what will the scale read?
1) less than 20 N 2) 20 N 3) between 20N and 29N 4) 29 N 5) greater than 29 N |
4) 29 N
The buoyant force is equal to the weight of the displaced fluid. Thus, the reduction in the “apparent” weight of the cylinder when it is submerged is exactly equal to the weight of the water that overflowed. When that water is poured back into the pail, the total weight returns to its original value of 29 N. |
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A boat carrying a large chunk of steel is floating on a lake. The chunk is then thrown overboard and sinks. What happens to the water level in the lake (with respect to the shore)?
1) rises 2) drops 3) remains the same 4) depends on the size of the steel |
2) drops
Initially the chunk of steel “floats” by sitting in the boat. The buoyant force is equal to the weight of the steel, and this will require a lot of displaced water to equal the weight of the steel. When thrown overboard, the steel sinks and only displaces its volume in water. This is not so much water -- certainly less than before -- and so the water level in the lake will drop. |
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An object floats in water with 3/4 of its volume submerged. What is the ratio of the density of the object to
that of water? 1) 1/4 2) 1/3 3) 4/3 4) 3/4 5) 2/1 |
4) 3/4
Remember that we have: Vfluid/Vobject = ρobject/ρfluid so if the ratio of the volume of the displaced water to the volume of the object is 3/4, the object has 3/4 the density of water. The object is now placed in oil with a density half that of water. What happens? 1) it floats just as before 2) it floats higher in the water 3) it floats lower in the water 4) it sinks to the bottom |
4) it sinks to the bottom
We know from before that the object has 3/4 the density of water. If the water is now replaced with oil, which has 1/2 the density of water, the density of the object is larger than the density of the oil. Therefore, it must sink to the bottom. |
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An object floats in water with 3/4 of its volume submerged. When more water is poured on top of the water, the object will:
1) move up slightly 2) stay at the same place 3) move down slightly 4) sink to the bottom 5) float to the top |
5) float to the top
We already know that density of the object is 3/4 of the density of water, so it floats in water (i.e., the buoyant force is greater than its weight). When covered by more water, it must therefore float to the top. |
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A blood platelet drifts along with the flow of blood through an artery that is partially blocked. As the platelet moves from the wide region into the narrow region, the blood pressure:
1) increases 2) decreases 3) stays the same 4) drops to zero |
2) decreases
The speed increases in the narrow part, according to the continuity equation. Since the speed is higher, the pressure is lower, from Bernoulli’s principle. |
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A person’s blood pressure is generally measured on the arm, at approximately the same level as the heart. How would the results differ if the measurement were made on the person’s leg instead?
1) blood pressure would be lower 2) blood pressure would not change 3) blood pressure would be higher |
3) Blood pressure would be higher
Assuming that the flow speed of the blood does not change, then Bernoulli’s equation indicates that at a lower height, the pressure will be greater. |
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How is the smoke drawn up a chimney affected when there is a wind blowing outside?
1) smoke rises more rapidly in the chimney 2) smoke is unaffected by the wind blowing 3) smoke rises more slowly in the chimney 4) smoke is forced back down the chimney |
1) smoke rises more rapidly in the chimney
Due to the speed of the wind at the top of the chimney, there is a relatively lower pressure up there as compared to the bottom. Thus, the smoke is actually drawn up the chimney more rapidly, due to this pressure difference. |
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A 1 kg ball is hung at the end of a rod 1 m long. If the system balances at a point on the rod 0.25 m from the end holding the mass, what is the mass of the rod?
1) 1/4 kg 2) 1/2 kg 3) 1kg 4) 2kg 5) 4kg |
3) 1 kg
The total torque about the pivot must be zero !! The CM of the rod is at its center, 0.25 m to the right of the pivot. Since this must balance the ball, which is the same distance to the left of the pivot, the masses must be the same !! |
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Bonnie sits on the outer rim of a merry-go-round, and Klyde sits midway between the center and the rim. The merry-go-round makes one complete revolution every two seconds.
Klyde’s angular velocity is: A) same as Bonnie’s B) twice Bonnie’s C) half of Bonnie’s D) 1/4 of Bonnie’s E) four times Bonnie’s |
A) same as Bonnie's
The angular velocity ω of any point on a solid object rotating about a fixed axis is the same. Both Bonnie & Klyde go around one revolution (2π radians) every two seconds. |
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Bonnie sits on the outer rim of a merry-go-round, and Klyde sits midway between the center and the rim. The merry-go-round makes one revolution
Who has the larger liner (tangential) velocity? A) Klyde B) Bonnie C) both the same D) linear velocity is zero for both of them |
B) Bonnie
Their linear speeds v will be different since v = Rω and Bonnie is located further out (larger radius R) than Klyde. |
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Suppose that the speedometer of a truck is set to read the linear speed of the truck, but uses a device that actually measures the angular speed of the tires. If larger diameter tires are mounted on the truck instead, how will that affect the speedometer reading as compared to the true linear speed of the truck?
A) speedometer reads a higher speed than the true linear speed B) speedometer reads a lower speed than the true linear speed C) speedometer still reads the true linear speed |
B) speedometer reads a lower speed than the true linear speed
The linear speed is v = ωR. So when the speedometer measures the same angular speed ω as before, the linear speed v is actually higher, because the tire radius is larger than before. |
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An object at rest begins to rotate with a constant angular acceleration. If this object rotates through an angle θ in the time t, through what angle did it rotate in the time1/2t?
A) 1/2 θ B) 1/4 θ C) 3/4 θ D) 2 θ E) 4θ |
B) 1/4 θ
The angular displacement is θ = 1/2 αt 2 (starting from rest), and there is a quadratic dependence on time. Therefore, in half the time, the object has rotated through one-quarter the angle. |
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An object at rest begins to rotate with a constant angular acceleration. If this object has angular velocity ω at time t, what was its angular velocity at the time 1/2 t?
A) 1/2 ω B) 1/4 ω C) 3/4 ω D) 2 ω E) 4 ω |
A) 1/2 ω
The angular velocity is ω = αt (starting from rest), and there is a linear dependence on time. Therefore, in half the time, the object has accelerated up to only half the speed. |
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You are using a wrench to loosen a rusty nut. What will be the most effective in loosening the nut?
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Since the forces are all the same, the only difference is the lever arm. The arrangement with the largest lever arm will
provide the largest torque. |
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Two forces produce the same torque. Does it follow that they have the same magnitude?
A) Yes B) No C) Depends |
B) No
Because torque is the product of force times distance, two different forces that act at different distances could still give the same torque. |
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If two torques are identical, does that mean their forces are identical as well?
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Because torque is the product of force times distance, a small force applied over a long distance could produce the same torque as a large force applied over a short distance
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A box is being pulled across a rough floor at a constant speed.
What can you say about the work done by friction? A) friction does no work at all B) friction does negative work C) friction does positive work |
B) friction does negative work
Friction acts in the opposite direction to the displacement, so the work is negative. Or using the definition of work: W = F d cos θ sinceθ=180o, then W<0. |
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Can friction ever do positive work?
A) yes B) no |
A) yes
Consider the case of a box on the back of a pickup truck. If the box moves along with the truck, then it is actually the force of friction that is making the box move. |
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In a baseball game, the catcher stops a 90-mph pitch. What can you say about the work done by the catcher on the ball?
A) catcher has done positive work B) catcher has done negative work C) catcher has done zero work |
B) catcher has done negative work
The force exerted by the catcher is opposite in direction to the displacement of the ball, so the work is negative. Or using the definition of work (W = Fd cos θ ), since θ = 180º, then W < 0. Note that because the work done on the ball is negative, its speed decreases. |
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A ball tied to a string is being whirled around in a circle.
What can you say about the work done by tension? A) tension does no work at all B) tension does negative work C) tension does positive work |
A) Tension does no work at all
No work is done because the force acts in a perpendicular direction to the displacement. Or using the definition of work: W = F d cos θ sinceθ=90º, then W=0. |
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A box is being pulled up a rough incline by a rope connected to a pulley. How many forces are DOING WORK on the box?
A) one force B) two forces C) three forces D) four forces E) no forces are doing work |
C) three forces
Any force not perpendicular to the motion will do work: N does no work T does positive work f does negative work mg does negative work |
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You lift a book with your hand in such a way that it moves up at constant speed. While it is moving, what is the total work done on the book?
A) mg×Δr B) FHAND × Δr C) (FHAND + mg) × Δr D) zero E) none of the above |
D) zero
The total work is zero since the net force acting on the book is zero. The work done by the hand is positive, while the work done by gravity is negative. the sum of the two is zero. Note that the kinetic energy of the book does not change, either! |
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By what factor does the kinetic energy of a car change when its speed is tripled?
A) no change at all B) factor of 3 C) factor of 6 D) factor of 9 E) factor of 12 |
D) factor of 9
Since the kinetic energy is ½mv², if the speed increases by a factor of 3, then the KE will increase by a factor of 9. |
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Car#1 has twice the mass of car#2,but they both have the same kinetic energy. How do their speeds compare?
A) 2v₁ = v₂ B) √2v₁ = v₂ C) 4 v₁ = v₂ D) v₁ = v₂ E) 8v₁ =v₂ |
B) √2v₁ = v₂
Since the kinetic energy is ½mv², and the mass of car #1 is greater, then car #2 must be moving faster. If the ratio of m₁/m₂ is 2, then the ratio of v2 values must also be 2. This means that the ratio of v₂/v₁ must be the square root of 2. |
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Two stones, one twice the mass of the other, are dropped from a cliff. Just before hitting the ground, what is the kinetic energy of the heavy stone compared to the light one?
A) quarter as much B) half as much C) the same D) twice as much E) four times as much |
D) twice as much
Consider the work done by gravity to make the stone fall distance d: ΔKE = Wnet = Fdcosθ ΔKE = mgd Thus, the stone with the greater mass has the greater KE, which is twice as big for the heavy stone. |
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A heavy stone and a light stone are dropped from the same height. Just before hitting the ground, what is the final speed of the heavy stone compared to the light one?
A) quarter as much B) half as much C) the same D) twice as much E) four times as much |
C) the same
All freely falling objects fall at the same rate, which is g. Since the acceleration is the same for both, and the distance is the same, then the final speeds will be the same for both stones. |
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A child on a skateboard is moving at a speed of 2 m/s. After a force acts on the child, her speed is 3 m/s. What can you say about the work done by the external force on the child?
A) positive work was done B) negative work was done C) zero work was done |
A) positive work was done
The kinetic energy of the child increased because her speed increased. This increase in KE was the result of positive work being done. Or, from the definition of work, sinceW=ΔKE=KEf –KEi andweknowthatKEf >KEi in this case, then the work W must be positive. |
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If a car traveling 60 km/hr can brake to a stop within 20 m, what is its stopping distance if it is traveling 120 km/hr? Assume that the braking force is the same in both cases.
A) 20m B) 30m C) 40m D) 60m E) 80m |
E) 80m
Fd =Wnet = ΔKE = 0–1/2 mv² thus: |F| d = 1/2 mv² Therefore, if the speed doubles, the stopping distance gets four times larger. |
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A car starts from rest and accelerates to 30mph. Later,it gets on a highway and accelerates to 60 mph. Which takes more energy, the 0→30 mph, or the 30→60 mph?
A) 0 → 30mph B) 30 → 60 mph C) both the same |
B) 30 → 60 mph
The change in KE (1/2 mv²) involves the velocity squared. So in the first case, we have: 1/2 m (30² - 0B) = 1/2 m (900) In the second case, we have: 1/2 m (60² - 30B) = 1/2 m (2700) Thus, the bigger energy change occurs in the second case. |
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The work W₀ accelerates a car from 0 to 50 km/hr. How much work is needed to accelerate the car from 50 km/hr to 150 km/hr?
A) 2W₀ B) 3W₀ C) 6W₀ D) 8W₀ E) 9W₀ |
D) 8W₀
Let’s call the two speeds v and 3v, for simplicity. We know that the work is given by: W=ΔKE=KEf –KEi Case#1: W₀ = 1/2m(v2² –0B) = 1/2m(vB) Case#2: W= 1/2m(3v)² –vB) = 1/2m(9v² –vB) = 1/2m(8vB) = 8W₀ |
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Two blocks of mass m₁ and m₂ (m₁ > m₂) slide on a frictionless floor and have the same kinetic energy when they hit a long rough stretch (μ > 0), which slows them down to a stop. Which one goes farther?
A) m1 B) m2 C) they will go the same distance |
B) m₂
With the same ΔKE, both block must have the same work done to them by friction. The friction force is less for m₂ so stopping distance must be greater. |
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A golfer making a putt gives the ball an initial velocity of v0, but he has badly misjudged the putt, and the ball only travels one-quarter of the distance to the hole. If the resistance force due to the grass is constant, what speed should he have given the ball (from its original position) in order to make it into the hole?
A) 2 v₀ B) 3 v₀ C) 4 v₀ D) 8 v₀ E) 16 v₀ |
A) 2 v₀
In traveling 4 times the distance, the resistive force will do 4 times the work. Thus, the ball’s initial KE must be 4 times greater in order to just reach the hole — this requires an increase in the initial speed by a factor of 2, since KE = 1/2 mv². |
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Is it possible for the kinetic energy of an object to be negative?
A) yes B) no |
B) no
The kinetic energy is 1/2 mv². The mass and the velocity squared will always be positive, so KE must always be positive. |
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Is it possible for the gravitational potential energy of an object to be negative?
A) yes B) no |
A) yes
Gravitational PE is mgh, where height h is measured relative to some arbitrary reference level where PE = 0. For example, a book on a table has positive PE if the zero reference level is chosen to be the floor. However, if the ceiling is the zero level, then the book has negative PE on the table. It is only differences (or changes) in PE that have any physical meaning. |
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You and your friend both solve a problem involving a skier going down a slope, starting from rest. The two of you have chosen different levels for y = 0 in this problem. Which of the following quantities will you and your friend agree on?
A) skier’s PE B) skier’s change in PE C) skier’s final KE D) only A and C E) only B and C |
E) only B and C
The gravitational PE depends upon the reference level, but the difference ΔPE does not! The work done by gravity must be the same in the two solutions, so ΔPE and ΔKE should be the same. |
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Two paths lead to the top of a big hill. One is steep and direct, while the other is twice as long but less steep. How much more potential energy would you gain if you take the longer path?
A) the same B) twice as much C) four times as much D) half as much E) yougainnoPEin either case |
A) the same
Since your vertical position (height) changes by the same amount in each case, the gain in potential energy is the same. |
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How does the work required to stretch a spring 2 cm compare with the work required to stretch it 1 cm?
A) same amount of work B) twice the work C) 4 times the work D) 8 times the work |
C) 4 times the work
The elastic potential energy is 1/2 kx². So in the second case, the elastic PE is 4 times greater than in the first case. Thus, the work required to stretch the spring is also 4 times greater. |
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A mass attached to a vertical spring causes the spring to stretch and the mass to move downwards. What can you say about the spring’s potential energy (PEs) and the gravitational potential energy (PEg) of the mass?
A) both PEs and PEg decrease B) PEs increases and PEg decreases C) both PEs and PEg increase D) PEs decreases and PEg increases E) PEs increases and PEg is constant |
B) PEs increases and PEg decreases
The spring is stretched, so its elastic PE increases, since PEs = 1/2 kx². The mass moves down to a lower position, so its gravitational PE decreases, since PEg = mgh. |
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Three balls of equal mass start from rest and roll down different ramps. All ramps have the same height. Which ball has the greater speed at the bottom of its ramp?
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same speed for all balls
All of the balls have the same initial gravitational PE, since they are all at the same height (PE = mgh). Thus, when they get to the bottom, they all have the same final KE, and hence the same speed (KE = 1/2 mvB). |
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A truck, initially at rest, rolls down a frictionless hill and attains a speed of 20 m/s at the bottom. To achieve a speed of 40 m/s at the bottom, how many times higher must the hill be?
A) half the height B) the same height C) √ 2 times the height D) twice the height E) four times the height |
E) four times the height
Use energy conservation: initial energy: Ei = PEg = mgH final energy: Ef = KE = 1/2 mv² Conservation of Energy: Ei = mgH = Ef =1/2mv² therefore: gH = 1/2v² So if v doubles, H quadruples! |
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A box sliding on a frictionless flat surface runs into a fixed spring, which compresses a distance x to stop the box. If the initial speed of the box were doubled, how much would the spring compress in this case?
A) half as much B) the same amount C) √ 2 times as much D) twice as much E) four times as much |
Use energy conservation:
initial energy: Ei = KE = 1/2mv² final energy: Ef = PEs = 1/2 kx² Conservation of Energy: Ei = 1/2mv² = Ef = 1/2kx² therefore: mv² = kx² So if v doubles, x doubles! |
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You see a leaf falling to the ground with constant speed. When you first notice it, the leaf has initial total energy PEi +KEi. You watch the leaf until just before it hits the ground, at which point it has final total energy PEf + KEf. How do these total energies compare?
A) PEi + KEi > PEf + KEf B) PEi +KEi = PEf + KEf C) PEi + KEi < PEf + KEf D) impossible to tell from the information provided |
A) PEi + KEi > PEf + KEf
As the leaf falls, air resistance exerts a force on it opposite to its direction of motion. This force does negative work, which prevents the leaf from accelerating. This frictional force is a non-conservative force, so the leaf loses energy as it falls, and its final total energy is less than its initial total energy. |
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You throw a ball straight up into the air. In addition to gravity, the ball feels a force due to air resistance. Compared to the time it takes the ball to go up, the time it takes to come back down is:
A) smaller B) the same C) greater |
C) greater
Due to air friction, the ball is continuously losing mechanical energy. Therefore it has less KE (and consequently a lower speed) on the way down. This means it will take more time on the way down !! |
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Mike applied 10 N of force over 3 m in 10 seconds. Joe applied the same force over the same distance in 1 minute. Who did more work?
A) Mike B) Joe C) both did the same work |
C) both did the same work
Both exerted the same force over the same displacement. Therefore, both did the same amount of work. Time does not matter for determining the work done. |
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Mike performed 5 J of work in 10 secs. Joe did 3 J of work in 5 secs. Who produced the greater power?
A) Mike produced more power B) Joe produced more power C) both produced the same amount of power |
B) Joe produced more power
Since power = work / time, we see that Mike produced 0.5 W and Joe produced 0.6 W of power. Thus, even though Mike did more work, he required twice the time to do the work, and therefore his power output was lower. |
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Engine #1 produces twice the power of engine #2. Can we conclude that engine #1 does twice as much work as engine #2?
A) yes B) no |
No!! We cannot conclude anything about how much work each engine does. Given the power output, the work will depend upon how much time is used. For example, engine #1 may do the same amount of work as engine #2, but in half the time.
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When you pay the electric company by the kilowatt-hour, what are you actually paying for?
A) energy B) power C) current D) voltage E) none of the above |
A) energy
We have defined: Power = energy / time So we see that: Energy = power x time This means that the unit of power x time (watt-hour) is a unit of energy !! |
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Which contributes more to the cost of your electric bill each month, a 1500-Watt hair dryer or a 600-Watt microwave oven?
A) hair dryer B) microwave oven C) both contribute equally D) depends upon what you cook in the oven E) depends upon how long each one is on |
E) depends upon how long each one is on
We already saw that what you actually pay for is energy. To find the energy consumption of an appliance, you must know more than just the power rating — you have to know how long it was running. |
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An open cart rolls along a
frictionless track while it is raining. As it rolls, what happens to the speed of the cart as the rain collects in it? (assume that the rain falls vertically into the box) A) speeds up B) maintains constant speed C) slows down D) stops immediately |
C) slows down
Since the rain falls in vertically, it adds no momentum to the box, thus the box’s momentum is conserved. However, since the mass of the box slowly increases with the added rain, its velocity has to decrease. |
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A system of particles is known to have a total kinetic energy of zero. What can you say about the total momentum of the system?
A) momentum of the system is positive B) momentum of the system is negative C) momentum of the system is zero D) you cannot say anything about the momentum of the system |
C) momentum of the system is zero
Since the total kinetic energy is zero, this means that all of the particles are at rest (v = 0). Therefore, since nothing is moving, the total momentum of the system must also be zero. |
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A system of particles is known to have a total momentum of zero. Does it necessarily follow that the total kinetic energy of the system is also zero?
A) yes B) no |
B) no
Momentum is a vector, so the fact that ptot = 0 does not mean that the particles are at rest! They could be moving such that their momenta cancel out when you add up all of the vectors. In that case, since they are moving, the particles would have non-zero KE. |
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Two objects are known to have the same momentum. Do these two objects necessarily have the same kinetic energy?
A) yes B) no |
B) no
If object #1 has mass m and speed v, and object #2 has mass 1/2 m and speed 2v, they will both have the same momentum. However, since KE = 1/2 mv2, we see that object #2 has twice the kinetic energy of object #1, due to the fact that the velocity is squared. |
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A net force of 200 N acts on a 100-kg boulder, and a force of the same magnitude acts on a 130-g pebble. How does the rate of change of the boulder’s momentum compare to the rate of change of the pebble’s momentum?
A) greater than B) less than C) equal to |
C) equal to
The rate of change of momentum is, in fact, the force. Remember that F = Δp/Δt. Since the force exerted on the boulder and the pebble is the same, then the rate of change of momentum is the same. |
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A net force of 200 N acts on a 100-kg boulder, and a force of the same magnitude acts on a 130-g pebble. How does the rate of change of the boulder’s velocity compare to the rate of change of the pebble’s velocity?
A) greater than B) less than C) equal to |
B) less than
The rate of change of velocity is the acceleration. Remember that a = Δv/Δt. The acceleration is related to the force by Newton’s 2nd Law (F = ma), so the acceleration of the boulder is less than that of the pebble (for the same applied force) because the boulder is much more massive. |
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A small car and a large truck collide head-on and stick together. Which one has the larger momentum change?
A) the car B) the truck C) they both have the same momentum change D) can’t tell without knowing the final velocities |
C) they both have the same momentum change
Since the total momentum of the system is conserved, that means that Δp = 0 for the car and truck combined. Therefore, Δpcar must be equal and opposite to that of the truck (–Δptruck) in order for the total momentum change to be zero. Note that this conclusion also follows from Newton’s 3rd Law. |
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Two boxes, one heavier than the other, are initially at rest on a horizontal frictionless surface. The same constant force F acts on each one for exactly 1 second. Which box has more momentum after the force acts?
A) the heavier one B) the lighter one C) both the same |
C) both the same
We know: Favg = Δp/Δt so impulse Δp = Fav Δt. In this case F and Δt are the same for both boxes ! Both boxes will have the same final momentum. |
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In the previous question, which box has the larger velocity after the force acts?
A) the heavier one B) the lighter one C) both the same |
B) the lighter one
The force is related to the acceleration by Newton’s 2nd Law (F = ma). The lighter box therefore has the greater acceleration, and will reach a higher speed after the 1-second time |
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You drive around a curve in a narrow one-way street at 30 mph when you see an identical car heading straight toward you at 30 mph. You have two options: hit the car head-on or swerve into a massive concrete wall (also head-on). What should you do?
A) hit the other car B) hit the wall C) makes no difference D) call your physics prof!! E) get insurance! |
C) makes no difference
In both cases your momentum will decrease to zero in the collision. Given that the time Δt of the collision is the same, then the force exerted on YOU will be the same!! If a truck is approaching at 30 mph, then you’d be better off hitting the wall in that case. On the other hand, if it’s only a mosquito, well, you’d be better off running him down... |
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A small beanbag and a bouncy rubber ball are dropped from the same height above the floor. They both have the same mass. Which one will impart the greater impulse to the floor when it hits?
A) the beanbag B) the rubber ball C) both the same |
B) the rubber ball
Both objects reach the same speed at the floor. However, while the beanbag comes to rest on the floor, the ball bounces back up with nearly the same speed as it hit. Thus, the change in momentum for the ball is greater, because of the rebound. |
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A person stands under an umbrella during a rainstorm. Later the rain turns to hail, although the number of “drops” hitting the umbrella per time and their speed remains the same. Which case requires more force to hold the umbrella?
A) when it is hailing B) when it is raining C) same in both cases |
A) when it is hailing
When the raindrops hit the umbrella, they tend to splatter and run off, whereas the hailstones hit the umbrella and bounce back upwards. Thus, the change in momentum (impulse) is greater for the hail. Since Δp = F Δt, more force is required in the hailstorm. |
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A bowling ball and a ping-pong ball are rolling toward you with the same momentum. If you exert the same force to stop each one, which takes a longer time to bring to rest?
A) the bowling ball B) same time for both C) the ping-pong ball D) impossible to say |
B) same time for both
Here, F and Δp are the same for both balls! It will take the same amount of time to stop them. |
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A bowling ball and a ping-pong ball are rolling toward you with the same momentum. If you exert the same force to stop each one, for which is the stopping distance greater?
A) the bowling ball B) same distance for both C) the ping-pong ball D) impossible to say |
C) the ping pong ball
Use the work-energy theorem: W = ΔKE. The ball with less mass has the greater speed (why?), and thus the greater KE (why again?). In order to remove that KE, work must be done, where W = Fd. Since the force is the same in both cases, the p distance needed to stop the less massive ball must be bigger. |
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Consider two elastic collisions:
A) a golf ball with speed v hits a stationary bowling ball head-on. B) a bowling ball with speed v hits a stationary golf ball head-on. In which case does the golf ball have the greater speed after the collision? A) situation 1 B) situation 2 C) both the same |
B) situation 2
Remember that the magnitude of the relative velocity has to be equal before and after the collision! In case 1 the bowling ball will almost remain at rest, and the golf ball will bounce back with speed close to v. In case 2 the bowling ball will keep going with speed close to v, hence the golf ball will rebound with speed close to 2v. |
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Carefully place a small rubber ball (mass m) on top of a much bigger basketball (mass M) and drop these from some height h. What is the velocity of the smaller ball after the basketball hits the ground, reverses direction, and then collides with small rubber ball?
A) zero B)v C) 2v D) 3v E) 4v |
D) 3v
Remember that relative velocity has to be equal before and after collision! Before the collision, the basketball bounces up with v and the rubber ball is coming down with v, so their relative velocity is –2v. After the collision, it therefore has to be +2v!! |
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You tee up a golf ball and drive it down the fairway. Assume that the collision of the golf club and ball is elastic. When the ball leaves the tee, how does its speed compare to the speed of the golf club?
A) greater than B) less than C) equal to |
A) greater than
This is exactly the same thing as situation #2 in a previous question. If the speed of approach (for the golf club and ball) is v, then the speed of recession must also be v. Since the golf club is hardly affected by the collision and it continues with speed v, then the ball must fly off with a speed of 2v. |
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A box slides with initial velocity 10 m/s on a frictionless surface and collides inelastically with an identical box. The boxes stick together after the collision. What is the final velocity?
A) 10 m/s B) 20 m/s C) 0 m/s D) 15 m/s E) 5 m/s |
E) 5 m/s
he initial momentum is: Mvi =(10)M The final momentum is: Mtotal vf = (2M) vf = (2M)(E) The final momentum must be the same!! |
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On a frictionless surface, a sliding box collides and sticks to a second identical box which is initially at rest. What is the final KE of the system in terms of the initial KE?
A) KEf = KEi B) KEf = KEi / 4 C) KEf = KEi / √ 2 D) KEf = KEi/2 E) KEf =√2KEi |
D) KEf = KEi/2
Momentum: mvi + 0 = (2m)vf So we see that: vf =1/2vi Now, look at kinetic energy: First, KEi = 1/2 mvi² So: KEf = 1/2 mfvf² = 1/2 (2m) (1/2 vi)² =1/2 (1/2 mvi²) = 1/2 KEi |
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A uranium nucleus (at rest) undergoes fission and splits into two fragments, one heavy and the other light. Which fragment has the greater momentum?
A) the heavy one B) the light one C) both have the same momentum D) impossible to say |
C) both have the same momentum
The initial momentum of the uranium was zero, so the final total momentum of the two fragments must also be zero. Thus the individual momenta are equal in magnitude and opposite in direction. |
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A uranium nucleus (at rest) undergoes fission and splits into two fragments, one heavy and the other light. Which fragment has the greater speed?
A) the heavy one B) the light one C) both have the same speed D) impossible to say |
B) the light one
We have already seen that the individual momenta are equal and opposite. In order to keep the magnitude of momentum mv the same, the heavy fragment has the lower speed and the light fragment has the greater speed. |
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A cannon sits on a stationary railroad flatcar with a total mass of 1000 kg. When a 10-kg cannon ball is fired to the left at a speed of 50 m/s, what is the recoil speed of the flatcar?
A) 0 m/s B) 0.5 m/s to the right C) 1 m/s to the right D) 20 m/s to the right E) 50 m/s to the right |
B) 0.5 m/s to the right
Since the initial momentum of the system was zero, the final total momentum must also be zero. Thus, the final momenta of the cannon ball and the flatcar must be equal and opposite. pcannonball = (10 kg)(50 m/s) = 500 kg-m/s pflatcar = 500 kg-m/s = (1000 kg)(0.5 m/s) |
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When a bullet is fired from a gun, the bullet and the gun have equal and opposite momenta. If this is true, then why is the bullet deadly? (whereas it is safe to hold the gun while it is fired)
A) it is much sharper than the gun B) it is smaller and can penetrate your body C) it has more kinetic energy than the gun D) it goes a longer distance and gains speed E) it has more momentum than the gun |
C) it has more kinetic energy than the gun
While it is true that the magnitudes of the momenta of the gun and the bullet are equal, the bullet is less massive and so it has a much higher velocity. Since KE is related to v2, the bullet has considerably more KE and therefore can do more damage on impact. |
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If the velocity of a car is non-zero (v ≠ 0), can the acceleration of the car be zero?
1) yes 2) no 3) depends on the velocity |
Sure it can! An object moving with constant velocity has a non-zero velocity, but it has zero acceleration since the velocity is not changing.
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When throwing a ball straight up, which of the following is true about its velocity v and its acceleration a at the highest point in its path?
1) both v=0 and a=0 2) v≠0,but a=0 3) v=0, but a≠0 4) both v≠0 and a≠0 5) not really sure |
3) v=0, but a≠0
At the top, clearly v = 0 because the ball has momentarily stopped. But the velocity of the ball is changing, so its acceleration is definitely not zero! Otherwise it would remain at rest!! |
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You throw a ball straight up into the air. After it leaves your hand, at what point in its flight does it have the maximum value of acceleration
1) its acceleration is constant everywhere 2) at the top of its trajectory 3) halfway to the top of its trajectory 4) just after it leaves your hand 5) just before it returns to your hand on the way down |
1) constant everywhere
The ball is in free fall once it is released. Therefore, it is entirely under the influence of gravity, and the only acceleration it experiences is g, which is constant at all points. |
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Alice and Bill are at the top of a building. Alice throws her ball downward. Bill simply drops his ball. Which ball has the greater acceleration just after release?
1) Alice’s ball 2) it depends on how hard the ball was thrown 3) neither -- they both have the same acceleration 4) Bill’s ball |
3) neither, they both have the same
Both balls are in free fall once they are released, therefore they both feel the acceleration due to gravity (g). This acceleration is independent of the initial velocity of the ball. |
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You throw a ball upward with an initial speed of 10 m/s. Assuming that there is no air resistance, what is its speed when it returns to you?
1) more than 10 m/s 2) 10 m/s 3) less than 10 m/s 4) zero 5) need more information |
2) 10 m/s
The ball is slowing down on the way up due to gravity. Eventually it stops. Then it accelerates downward due to gravity (again). Since a = g on the way up and on the way down, the ball reaches the same speed when it gets back to you as it had when it left. |
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Alice and Bill are at the top of a cliff of heigh H. Both throw a ball with initial speed V₀, Alice straight down and Bill straight up. The speeds of the balls when they hit the ground are V₁ and V₂. If there is no air resistance, which is true?
1) V₁ < V₂ 2) V₁ > V₂ 3) V₁ = V₂ |
3) V₁ = V₂
Bill’s ball goes up and comes back down to Bill’s level. At that point, it is moving downward with v0, the same as Alice's ball. Thus, it will hit the ground with the same speed as Alice's ball. Thus, it will hit the ground with the same speed as Alice's ball. |
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You drop a rock off a bridge. When the rock has fallen 4 m, you drop a second rock. As the two rocks continue to fall, what happens to their separation?
1) the separation increases as they fall 2) the separation stays constant at 4 m 3) the separation decreases as they fall 4) it is impossible to answer without more information |
1) the separation increases as they fall
At any given time, the first rock always has a greater velocity than the second rock, therefore it will always be increasing its lead as it falls. Thus, the separation will increase. |
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Ignoring air resistance, the horizontal component of a projectile's velocity
A) remains constant B) continuously increases C) continuously decreases D) is zero |
A) remains constant
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An object of mass m is hanging by a string from the ceiling of an elevator. The elevator is moving upward but slowing down. What is the tension in the string?
A) less than mg B) greater than mg C) zero D) exactly mg |
A) less than mg
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Objects A and B both start from rest. They both accelerate at the same rate. However, object A accelerates for twice the time as object B. What is the distance traveled by object A compared to that of object B?
A) three times as far B) the same distance C) twice as far D) four times as far |
D) four times as far
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Inertia is stubbornness to change in motion. The units for Inertia are:
A) Newton-meter B) Newtons C) Kilograms D) Acceleration |
C) Kilograms
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A package of supplies is dropped from a plane, and one second later a second package is dropped. Neglecting air resistance, the distance between the falling packages will
A) depend on their weight B) decrease C) increase D) be constant |
C) increase
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An object of mass m sits on a flat table. The Earth pulls on this object with force mg, which we will call the action force. What is the reaction force?
A) the object pulling upward on the Earth with force mg B) the object pushing down on the table with force mg C) the table pushing up on the object with force mg D) the table pushing down on the floor with force mg |
A) the object pulling upward on the Earth with force mg
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A brick and a feather are released in a vacuum and fall at the same rate. Which object experiences the greater gravitational force with the earth?
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A) the brick
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A ball is thrown straight up, reaches a maximum height, then falls to its initial height. Make a statement about the direction of the velocity and acceleration as the ball is coming down.
A) Both its velocity and its acceleration point downward B) Its velocity points upward and its acceleration points downward C) Its velocity points downward and its acceleration points upward D) Both its velocity and its acceleration point upward |
A) Both its velocity and its acceleration point downward
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The gravitational force between two objects is proportional to
A) the square of the distance between the two objects B) the product of the mass of the two objects C) the square of the product of the mass of the two objects D) the distance between the two objects |
B) the product of the mass of the two object
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An object hits a wall and bounces back with half of its original speed. What is the ration of the final kinetic energy to the initial kinetic energy?
A) 1/4 B) 4 C) 1/2 D) 2 |
A) 1/4
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The area under the curve on a Force versus time (F vs t) graph represents
A) work B) momentum C) impulse D) kinetic energy |
C) impulse
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A small object collides with a large object and sticks. Which object experiences the larger magnitude of momentum change?
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Both experience the same magnitude of momentum change
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Smoky the cat is relaxing on the arm of a couch, one meter above the ground, when he is startled by something and jumps straight up into the air with initial speed 4 m/s. Coming down, he misses the couch and lands on the ground. You can neglect air resistance in your answers.
What is smoky's acceleration: A) just after his paws leave the couch and he is on his way up? B) at the exact instant when he is at his maximum height? C) just before he hits the ground on his way back down? |
-9.8 m/s² throughout
on his way up he is decelerating in the positive direction on his way down he is accelerating in the negative direction |
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What are 3 different ways to change your velocity while driving your car?
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speeding up, slowing down, and changing direction
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A ball bounces on the ground.
How many forces are acting on it as it bounces (while it is in contact with the ground) |
TWO
Normal force and mg |
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You see a $20 bill on the ground and run forward to get it. What force accelerated you forward, and why?
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Friction, I push on the ground to go forward. Without friction NO MOVE (think ice)
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Famous astronaut Spiff Jones zips through interstellar space in a rocket-propelled spaceship. He is very distant from all massive bodies, so gravitational forces can be ignored. As the burnt fuel is expelled from the back of the rocket, how does the force the rocket exerts on the exhaust gases compare to the force the exhaust gases exert on the rocket?
How is Spiff accelerating? |
Newton's third law, equal and opposite forces.
Though gas has less mass and will go faster (accelerate faster) |
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A washing machine uses a spin cycle to rapidly remove large quantities of water from wet clothes. Give a physics description (i.e. in terms of forces, acceleration and Newton’s Laws) of how this works.
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Once it gets moving, the water in your clothes wants to continue in a straight line (1st law). In this case, when the washer starts to spin, the holes in the side allow the water to pass through because of its own intertia, and so the water escapes out the holes. Your clothes would to the same thing but the holes are too small
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Is it possible to whirl a ball (attached to a string) in a circle in the air with the string completely horizontal?
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Not possible
The ball on the string feels only 2 forces: the tension in the string and its own weight. If the string were horizontal, then there would be nothing to balance the downward force of weight, and the ball would descend. There must be some vertical component of tension to balance the weight, so the string must be at some angle to the horizontal |
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A pendulum is launched from a point that is a height h above its lowest point in two different ways. During both launches, the pendulum is given an initial speed of 3.0m/s. On the first launch, the initial velocity of the pendulum is directed upward along the trajectory, and on the second launch it is directed downward along the trajectory. Which launch will cause it to swing the largest angle from the equilibrium position? Explain.
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The two launches will result in the same largest angle. Applying conservation of energy between the launching point and the highest point, we have E1 = E2 = 1/2 mv² + mgh = mghmax .
The direction of the launching velocity does not matter, and so the same maximum height (and hence maximum angle) will results from both launches. Also, for the first launch, the ball will rise to some maximum height and then come back to the launch point with the same speed as when launched. That then exactly duplicates the second launch. |
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In a soap box derby, the cart starts form the top of the hill and coasts down to the bottom of the hill. State where the energy comes from for this motion and where the energy is going as the cart goes down the hill. Do not ignore friction.
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The energy of the cart at the top of the hill is the stored gravitational potential energy that came from the work it took to get the cart up the hill. As the cart coasts down the hill, the GPE is turned into Kinetic energy and heat from the frictional work done, the non-conservative work. GPE = KE + Energy Lost. The energy lost is the Frictional force times the distance traveled.
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Two points, P1 and P2, are rotating about the same point. What do the points have in common?
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Angle of rotation, rotational speed, and angular acceleration
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What force causes a ball to ROTATE as it rolls down a hill?
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Friction force
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