Physics Chapter 10

Front 1

projectile

Back 1

Any object that moves through the air or through space under the influence of gravity.

Front 2

parabola

Back 2

The curved path followed by a projectile under the influence only of constant gravity,

Front 3

satellite

Back 3

A projectile or small celestial body that orbits a larger celestial body.

Front 4

ellipse

Back 4

The oval path followed by a satellite. The sum of the distances from any point on the path to two points called foci is a constant. When the foci are together at one point, the ellipse is a circle. As the foci get farther apart, the ellipse becomes more "eccentric."

Front 5

Kepler's laws

Back 5

Law 1: The path of each planet around the Sun is an ellipse with the Sun at one focus.
Law 2: The line from the Sun to any planet sweeps out equal areas of space in equal time intervals.
Law 3: The Square of the orbital period of a planet is directly proportional to the cube of the average distance of the planet from the Sun.

Front 6

escape speed

Back 6

The speed that a projectile, space probe, or similar object must reach to escape the gravitational influence of Earth or of another celestial body to which it is attracted.

Front 7

At the instant a cannon fires a cannonball horizontally over a level range, another cannonball held at the side of the cannon is released and drops to the ground. Which ball,the one fired downrange or the one dropped from rest, strikes the ground first?

Back 7

Both cannonballs hit the ground at the same time, for both fall the same vertical distance. Notice that the physics is the same as shown in Figures 10.3 and 10.4. We can reason this another way by asking which one would hit the ground first if the cannon were pointed at an upward angle. Then the dropped cannonball would hit first, while the fired ball remains airborne. Now consider the cannon pointing downward. In this case, the fired ball hits first. So projected upward, the dropped one hits first; downward, the fired one hits first. Is there some angle at which there is a dead heat, where both hit at the same time? Can you see that this occurs when the cannon is horizontal?

Front 8

Suppose the cannonball in Figure 10.8 were fired faster. How many meters below the dashed line would it be at the end of the 5 s?

Back 8

The vertical distance beneath the dashed line at the end of 5 s is 125 m [d = 5t2 = 5( 5) 2 = 5( 25) = 125 m]. Interestingly enough, this distance doesn’t depend on the angle of the cannon. If air drag is neglected, any projectile will fall m below where it would have reached if there were no gravity.

Front 9

If the horizontal component of the cannonball’s velocity is 20 m/ s, how far downrange will the cannonball be in 5 s?

Back 9

With no air drag, the cannonball will travel a horizontal distance of 100 m [d = vt = ( 20 m/ s)( 5 s) = 100 m]. Note that, since gravity acts only vertically and there is no acceleration in the horizontal direction, the cannonball travels equal horizontal distances in equal times. This distance is simply its horizontal component of velocity multiplied by the time ( and not 5t2, which applies only to vertical motion under the acceleration of gravity).

Front 10

A baseball is batted at an angle into the air. Once airborne, and neglecting air drag, what is the ball’s acceleration vertically? Horizontally?

Back 10

Vertical acceleration is g because the force of gravity is vertical. Horizontal acceler-ation is zero because no horizontal force acts on the ball.

Front 11

At what part of its trajectory does the baseball have minimum speed?

Back 11

A ball’s minimum speed occurs at the top of its trajectory. If it is launched verti-cally, its speed at the top is zero. If launched at an angle, the vertical component of velocity is zero at the top, leaving only the horizontal component. So the speed at the top is equal to the horizontal component of the ball’s velocity at any point. Doesn’t this make sense?

Front 12

Consider a batted baseball following a parabolic path on a day when the Sun is directly overhead. How does the speed of the ball’s shadow across the field compare with the ball’s horizontal component of velocity?

Back 12

They are the same!

Front 13

The boy on the tower throws a ball 20 m downrange, as shown in Figure 10.15. What is his pitching speed?

Back 13

The ball is thrown horizontally, so the pitching speed is horizontal distance divided by time. A horizontal distance of 20 m is given, but the time is not stated. However, knowing the vertical drop is 5 m, you remember that a 5- m drop takes 1 s! From the equation for constant speed ( which applies to horizontal motion), v = d/ t, ( 20 m)/( 1 s) = 20 m/ s. It is interesting to note that the equation for constant speed, v = d/ t, guides our thinking about the crucial factor in this problem— the time.

Front 14

One of the beauties of physics is that there are usually different ways to view and explain a given phenomenon. Is the following explanation valid? Satellites remain in orbit instead of falling to Earth because they are beyond the main pull of Earth’s gravity.

Back 14

No, no, a thousand times no! If any moving object were beyond the pull of gravity, it would move in a straight line and would not curve around Earth. Satellites remain in orbit because they are being pulled by gravity, not because they are beyond it. For the altitudes of most Earth satellites, Earth’s gravitational field is only a few percent weaker than it is at Earth’s surface.

Front 15

True or false: The space shuttle orbits at altitudes in excess of 150 km to be above both gravity and Earth’s atmosphere.

Back 15

False. What satellites are above is the atmosphere and air resistance— not gravity! It’s important to note that Earth’s gravity extends throughout the universe in accord with the inverse- square law.

Front 16

Satellites in close circular orbit fall about 5 m during each second of orbit. Why doesn’t this distance accumulate and send satellites crashing into Earth’s surface?

Back 16

In each second, the satellite falls about 5 m below the straight- line tangent it would have followed if there were no gravity. Earth’s surface also curves 5 m beneath a straight- line 8- km tangent. The process of falling with the curvature of Earth continues from tangent line to tangent line, so the curved path of the satellite and the curve of Earth’s surface “ match” all the way around the planet. Satellites do, in fact, crash to Earth’s surface from time to time when they encounter air resistance in the upper atmosphere that decreases their orbital speed.

Front 17

The orbital path of a satellite is shown in the sketch. In which of the marked positions A through D does the satellite have the greatest speed? The lowest speed?

Back 17

The satellite has its greatest speed as it whips around position A and has its low-est speed at position C. After passing C, it gains speed as it falls back to A to repeat its cycle.

Front 18

The orbital path of a satellite is shown in the sketch. In which marked positions A through D does the satellite have the greatest KE? The greatest PE? The greatest total energy?

Back 18

KE is maximum at the perigee A; PE is maximum at the apogee C; the total energy is the same everywhere in the orbit.

Front 19

Why does the force of gravity change the speed of a satellite when it is in an elliptical orbit but not when it is in a circular orbit?

Back 19

In circular orbit, the gravitational force is always perpendicular to the orbital path. With no component of gravitational force along the path, only the direction of motion changes— not the speed. In elliptical orbit, however, the satellite moves in directions that are not perpendicular to the force of gravity. Then components of force do exist along the path, which change the speed of the satellite. A component of force along ( parallel to) the direction the satellite moves does work to change its KE.