A2 Physics - Further Mechanics (Brampton)

Front 1

For something to move in circular motion, what is the one condition that must be met?

Does this condition apply to all objects moving in circular motion?

Give 2 examples of where centripetal force can occur.

Draw a visual demonstration of a rock moving in circular motion due to it being swung around. Label the centripetal force (F), the object's velocity (v), and the angle between the force and velocity.

Back 1

A force (centripetal force) must constantly be acting at 90° to an object's velocity (towards the centre of the circle.)

This condition applies to ALL objects moving in circular motion.

E.g. Satellites moving around the earth, cars driving around a roundabout.

Front 2

Define Centripetal force.

Back 2

The force acting on an object that is ALWAYS towards the centre of the object's circular motion (Circular path).

Front 3

Define Centrifugal force.

Give an example of Centrifugal force using someone in a car.

What is is that's actually happening?

Back 3

the Fake force that you think you're feeling pushing you out when undergoing circular motion.

E.g. When you're in a car going around a roundabout.

What's actually happening is that you are just feeling the centripetal force pushing you into the circle's centre.

Front 4

Velocity is always (what) to the (what)

And (what) to the (what)?

Back 4

Velocity is ALWAYS perpendicular to the centripetal force

and at a tangent to the object's circular path.

Front 5

If the centripetal force were to stop, draw what will happen and explain briefly what is happening.

(Next question is on hint page after answering the first part)

Back 5

The object will fly off at a tangent to the circle with initial speed 'v'.

(Initial speed is 'v' since the object may fly off at an angle, so the speed 'v' may have to be resolved into its velocity vectors.)

Hint 5

Why will the object's initial speed be ' 'v' and not it's initial velocity?

Front 6

Where may Centripetal force be used for leisure?

Give 2 examples.

Back 6

In ferris wheels

In rollercoaster rides.

Front 7

Draw a visual demonstration of centripetal force on a ferris wheel.

Label the velocity and centripetal force.

Explain what the people on the wheel will feel and explain what is causing that feeling.

Back 7

People in the carts feel like they're being pushed out, but that is caused by the centripetal force pushing them in.

Front 8

Draw a visual demonstration of centripetal force on a rollercoaster ride.Label the velocity and centripetal force. Explain what the people on the rids will feel and explain what is causing that feeling.

Back 8

People on the ride will feel like they're being pushed out, but that is the centripetal force pushing them in.

Front 9

In circular motion, the circular path of the object has a radius 'r'. Why can the circular path of the object have a radius?

Back 9

Because the distance between the object and the circle's centre remains constant.

Front 10

In circular motion, the centripetal force is acting towards the centre of the circle. What else is acting towards the centre of the circle and why?

Back 10

The object's acceleration is acting towards the centre of the circle because force and acceleration are ALWAYS acting towards the centre of the circle.

Front 11

What is the equation for the acceleration of an object towards the centre of the circle (a)?

Back 11

a = v²/r

Front 12

What is the equation for centripetal force?

Explain why.

Back 12

F = (mv²)/r

The equation for resultant force is

F = ma

And a = v²/r. (Acceleration towards circles centre.)

Sub that expression for 'a' in.

Then you get F = (mv²)/r.

Front 13

What is the equation that relates frequency and time period?

Back 13

T = 1/f

Front 14

What are the different equations for perpendicular velocity (green) in circular motion?

Find all of them by subbing in different terms for others using different equations.

Back 14

Front 15

What is the symbol for angular velocity?

What is the equation for angular velocity?

What is the unit for angular velocity?

Write down the equation for the perpendicular velocity using the angular velocity.

Back 15

Front 16

Circular motion can happen in satellites. Draw a visual demonstration of a satellite undergoing circular motion.

Label the radius and draw the circular path only.

Where is the radius from to?

Let's assume this is geostationary orbit.

What is geostationary orbit?

Back 16

Radius is from the circle's edge to the CENTRE of the earth. (Circle's centre)

Geostationary orbit - orbit where the satellite remains still above the same point on the earth's surface (above the equator).

Front 17

For this geostationary orbit, let's say:

T = 24 hours (For 1 earth rotation)

r = 4.2 x 10^7m

m = 50kg.

Find the centripetal force felt by the satellite.

(Do it twice. First time without angular velocity and 2nd time with angular velocity.)

(Without angular velocity on hint card, with angular velocity on answer card.)

Back 17

With angular velocity

Hint 17

Without angular velocity

Front 18

Circular motion can also occur in planes. When a plane banks (Turns in a circle to change direction), it undergoes circular motion.

Draw a visual demonstration of a plane banking. Include it's path, the resultant force acting on the plane and it's direction, the horizontal and vertical components of that resultant force, and the angle between the resultant force and the horizontal force component as (Theta).

Back 18

Front 19

In this plane banking situation, what two forces are acting on the plane?

Why does the resultant force acting on the plane have a vertical component of mg?

Back 19

Gravity and centripetal force are acting on the plane.

The resultant force has a vertical component of mg because the plane remains on the same level. A force must be equal to and cancelling out the plane's weight, hence causing the diagonal resultant force due to the horizontal centripetal force and the vertical force equal to the weight.

Front 20

What other kind of vehicle will this plane model work for?

What will be the difference between that vehicles model and the planes model?

Back 20

This model will also work for a car going around a bend.

The difference is that the ↑mg is caused by the reaction force from the ground.

Front 21

How would you find F (resultant force)?

(There are 2 methods. Method 1 is on hint flashcard, method 2 is on answer flashcard)

Back 21

Hint 21

Front 22

Find the perpendicular velocity at which the plane travels with.

Back 22

If you want to find velocity 'v', make both the (resultant) force equations equal to each other then solve for 'v'.

Front 23

Circular motion also happens in a vehicle looping around a loop de loop.

Draw an example of this.

Do it at 3 positions. One at the bottom, one to the very right and one at the top. Label them 1, 2 and 3 respectfully.

and label the main force of relevance and where it goes towards. What is this force called?

Back 23

The force S is the support force

Front 24

At 1, what is the supoort force equal to and why?

Back 24

At 1, Support force = centripetal force + weight

Because at 1, the centripetal force is needed to keep the vehicle moving in a circular motion AND more support is needed to cancel out the weight.

Front 25

At 2, what is the supoort force equal to and why?

Back 25

Support force = centripetal force ONLY

since the weight of the object is at a tangent to the circle's centre. It's not acting towards or away from the circle centre so it isn't required.

Front 26

At 3, what is the supoort force equal to and why?

Back 26

At 3, support force = centripetal force - weight.

Because the weight is helping the centripetal force pull the vehicle towards the circle.

Front 27

Define Simple Harmonic Motion.

Back 27

When things oscillate about a fixed point due to:

1) Acceleration acting in the opposite direction to displacement

2) Acceleration being proportional to displacement. (a oc -x)

Front 28

Give an example of where Simple Harmonic Motion can occur.

Back 28

In swings.

Front 29

Draw a visual example of simple harmonic motion on a swing. Let the right direction be +ve and the left direction be -ve. Label the furthest right point as 1 and the furthest left point as 2. Also label equilibrium.

From 1 and 2 the object will return to equilibrium. Draw Where the force returning them to equilibrium will be acting. What is the force called?

Back 29

The force bringing the object back to equilibrium is called the Restoring Force!

Front 30

Look at the diagram. Simple harmonic motion is happening.

1) At equilibrium, will the person feel a force bringing them back to equilibrium? Why?

2) At 1, will the person feel a force trying to bring them back to equilibrium? What direction will the force be in? What will be causing the force?

3) At 2, will the person feel a force trying to bring them back to equilibrium? What direction will the force be in? What will be causing the force?

Back 30

1) At equilibrium, the person won't feel any force trying to bring them back to equilibrium because they ARE at equilibrium.

2) At 1, The person will feel a forward force trying to bring them back to equilibrium (the force is a component of their weight.)

3) At 2, The person will feel a backward force trying to bring them back to equilibrium (the force is a component of their weight).

Front 31

What are the 2 conditions needed for SHM to occur?

Give an example for the first condition using the diagram above.

Explain why the second condition involves a negative sign where it is.

Back 31

1) Acceleration (thus force) must act in the opposite direction to the displacement.

E.g. Look at the diagram above. When the person displaces to the right (1), displacement is +ve, SO acceleration (and force) is in the opposite direction, to the left (-ve).

When the person displaces to the right (2), displacement is -ve, so acceleration (and force) is in the opposite direction, to the right (-ve).

2) Acceleration is proportional to displacement (a oc -x)

(x is -ve since condition 1) states that acceleration must act in the opposite direction to displacement)

Front 32

The 2 conditions for SHM can be represented in an equation. What is the equation that represents the 2 conditions for SHM?

(In other words, what is the equation for acceleration in SHM?)

State what each part of the equation means and how you will find the frequency component in SHM.

(E.g. how will you find frequency if you start from one end? What about if you start in the middle?)

In this equation, what can frequency be replaced with?

Back 32

f is frequency (complete oscillations per second). In SHM, one complete oscillation is, for example, swinging from one end (1) to the other end (2) and back again (1), to the original position.

If you start from the middle 1 oscillation would be middle, to one end (2), to the other end (1) then back to the middle.

x Is displacement from equilibrium.

w is angular velocity.

In this equation, frequency can be replaced with 1/T. (T = time period for 1 oscillation)

Front 33

In SHM, 'A' is a component used in later equations.

What is 'A' and state what it means.

Back 33

A is amplitude (maximum displacement from equilibrium or the maximum value x can be)

Front 34

Complete the table. This is referring to the behaviour of the different components at different position in SHM.

Refer to the diagram if you need help on the hint card.

Just state if the component is a (0, max+, max- or max+-) at that position.

What two components will do the same thing?

What determines whether velocity is a max+ or a max-?

Back 34

Acceleration and force will do the same thing.

If at the centre the object is going right (+ve), max 'v' is +ve.

If at the centre the object is going left (-ve), max 'v' is -ve.

Hint 34

Front 35

You need to know the SHM graphs and equations for displacement, velocity and acceleration.

What does the displacement-time graph for circular motion look like?

Label the amplitude (A).

What is the equation for displacement from equilibrium (x)?

Back 35

Front 36

What does the velocity-time graph for SHM look like?

What is the equation for velocity in SHM?

What is the equation for Maximum velocity in SHM? (Remember, at centre, x = 0 and velocity is max)

Back 36

Front 37

What does the acceleration-time graph for SHM look like?

What is the equation for acceleration in SHM?

What is the equation for Maximum acceleration in SHM? (Replace x with A)

Back 37

Front 38

What is the relationship between the displacement, velocity and acceleration-time graphs?

Back 38

Displacement-time graph and velocity-time graph are pi/2 radians out of phase

Velocity-time graph and acceleration-time graph are pi/2 radians out of phase

Displacement-time graph and acceleration-time graph are pi radians out of phase.

Front 39

In what situation is the velocity equation for SHM useful?

Draw a situation where it will be useful.

Back 39

Velocity equation is useful with pendulums where the height difference between equilibrium and the maximum displacement (h) is given.

Front 40

When can SHM modelling and equations be used in pendulum-like systems?

Back 40

When the oscillating object is below 10° (<10°) from equilibrium.

Front 41

If you want to find amplitude, what 2 things must you use?

Algebraically find the amplitude, A.

Back 41

Max potential energy (potential energy at 1) and max kinetic energy (kinetic energy at 0) are equal.

To find amplitude, you must use

energy and maximum velocity.

Front 42

How would you find the tension in the string in SHM? (What is the equation you would use?) Why do you use these expressions?

Back 42

Front 43

You need to know the Energy-displacement graphs for SHM.

What does the Kinetic Energy-displacement graph look like for SHM?

What are the 2 things that the graph may do at the bottoms?

Back 43

At the bottoms, the graph may curve off to the bottom (like in the image) OR go straight to the bottom.

Front 44

Why is the Kinetic Energy-time graph at a maximum when x = 0?

Back 44

Because velocity is maximum when

x = 0, and

Ek = ½mv².

So Ek will be maximum when velocity is maximum.

Front 45

What does the Potenetial Energy-displacement graph look like for SHM?

What do the peaks of the Ep and Ek graphs have in common?

Back 45

Front 46

The total energy (Peak of Ek or Ep graph) in an SHM system should be constant (remain the same) unless what happens?

Back 46

Unless damping happens.

Front 47

What are the 2 specific cases of SHM I need to know about?

Back 47

Ball on a string (left-right SHM)

Mass on a spring (up-down SHM)

Front 48

For a left-right (E.g. ball on a string) SHM system, what is the equation for time period? State what each part of the equation means.

(Given in formula book)

Back 48

(Given in formula book)

T is time period

L is length of string

g is gravitational field strength

(9.8N/kg on earth)

Front 49

What 2 things are not in the equation for the time period of a ball on a string undergoing SHM?

What does this mean?

Back 49

No 'mass'

No 'amplitude' (maximum displacement).

This means that both the mass of the object and it's amplitude can be anything, but if all the components of the 'T' equation stay the same, 'T' will also stay the same.

Front 50

What components does the Time period (T) for a ball on a string SHM have?

How would you change T using these components?

Back 50

T has g (gravitational field strength). You can change T by doing SHM on another planet because g changes on different planets.

T also has L (length of string). You can change T by changing the length of the string.

Front 51

What is the relationship between T and the expressions in the picture, in terms of proportionality?

And under what circumstances are these proportionalities true?

Back 51

Front 52

Proportionality practice:

1) If L x 2, T x ?

2) If g ÷ 4, T ?

Back 52

Front 53

How would you find 'g' experimentally using a ball on a string? Give the steps.

Back 53

1) rearrange 'T' to find an equation for 'g' (Shown above)

2) grad = ∆y/∆x. T² is denominator, and L is part of numerator.

3) Plot T² against L.

4) find gradient (L/T²)

5) gradient x 4(pi)² = g

(L/T²) x 4(pi)² = g

Front 54

For a mass on a spring undergoing circular motion (up-down SHM), what is the equation for time period?

State what each part of the equation means.

Back 54

Front 55

What components are NOT in the T equation for the time period of a mass on a spring's SHM?

What does this mean?

Back 55

No 'g' (gravitational field strength)

No 'A' (Amplitude)

This means that T will remain the same if only g and A change. T will remain the same on any planet, with any Maximum displacement from equilibrium (any change in A).

Front 56

What is the relationship between T and the expressions in the picture, in terms of proportionality?

Under what circumstances are these proportionalities true?

Back 56

Front 57

Proportionality practice:

IF k x 4, T?

Back 57

Front 58

For mass on a spring SHM, explain how you would find 'k' experimentally using a mass on a spring. Explain the steps.

Back 58

1) Rearrange 'T' to find an equation for k. (Shown on hint flashcard)

2) grad = ∆y/∆x. T² is denominator, 'm' is part of numerator.

3) Plot T² against m.

4) Find gradient (m/T²)

5) gradient x 4(pi)² = k

(m/T²) x 4(pi)² = k

Hint 58

Front 59

What is Damping?

Back 59

When there is a resistive force opposing the motion of an object undergoing SHM.

Front 60

What direction is the resistive force in Damping ALWAYS IN?

Back 60

The resistive force is ALWAYS in the opposite direction to velocity.

Front 61

Simple harmonic motion can occur with a person on a swing.

1) If there was no drag force or air resistance, what would happen?

2) in reality, what will happen and why?

3) in reality, will the displacement-time graph for SHM look different compared to the earlier graph?

Back 61

1) if there was no drag force or air resistance, the person would swing forever.

2) in reality, the person's amplitude (maximum displacement from equilibrium) will decrease overtime and they will eventually stop because there is air resistance.

3) yes. The displacement-time graph for SHM will look different in reality compared to the earlier graph.

Front 62

What are the 3 types of damping?

Back 62

Light damping

Heavy damping

Critical damping

Front 63

What is light damping?

Draw what the displacement-time graph for an SHM system undergoing light damping will look like.

Back 63

Light Damping: Damping where amplitude decreases over time and the change to time period is negligible so it stays the same.

Front 64

What is heavy damping? Draw what the displacement-time graph for an SHM system undergoing heavy damping will look like.

Back 64

Heavy damping: Damping where a force is applied that doesn't let the object oscillate, but instead brings it'd displacement down to zero very slowly.

Front 65

What is critical damping? Draw what the displacement-time graph for an SHM system undergoing critical damping will look like.

Back 65

Critical damping: Damping where a massive force quickly brings an SHM system to equilibrium.

Front 66

What is the opposite of Damping?

(What can support the motion of an object undergoing SHM?)

Back 66

Resonance (A driving force)

Front 67

In what direction is the force caused by resonance?

Back 67

In the same direction as velocity

Front 68

What does resonance do to the amplitude and velocity of an object undergoing SHM?

Back 68

Resonance increases amplitude and velocity of an object undergoing SHM.

Front 69

To successfully increase the velocity and amplitude of an object undergoing SHM, what 3 characteristics must the force caused by resonance have?

Back 69

- The force must be in the same direction as velocity

- The force should have the same (or a similar) frequency as the natural/resonant frequency (The frequency the system would oscillate with if there were NO external forces)

- The force must be 90° or (pi)/2 radians out of phase with the restoring force

Front 70

If the frequency of the driving force caused by resonance is a multiple of the natural/resonant frequency, what will happen to the resonant frequency?

E.g. driving force's freq = 2(resonant freq)

What is the new resonant frequency equal to?

Back 70

The resonant frequency will change by that multiple.

E.g. driving force's freq = 2(resonant freq)

New resonant freq = (resonant freq) x 2.