Chapter 5 Mastering Physics

In the previous part, you found that a pumpkin fired with an initial speed of 22 m/sm/s and an angle of 40∘40∘ reaches the same height as a pumpkin fired vertically with an initial speed of 14 m/sm/s. Which pumpkin takes longer to land?

Both pumpkins are in the air the same amount of time.

Rank from greatest to least their times to orbit Earth. Rank from greatest to least. To rank items as equivalent, overlap them.

CBA

The following diagrams are the same as those from Part A. Again considering only the two objects shown in each pair, this time rank the strength, from strongest to weakest, of the gravitational force acting on the object on the right.

- asteroid:sun - asteroid:earth - asteroid:moon - asteroid:asteroid - asteroid:hydrogen atom

The following diagrams are the same as those from Part A. This time, rank the pairs from left to right based on the size of the acceleration the asteroid on the left would have due to the gravitational force exerted on it by the object on the right, from largest to smallest.

- asteroid:sun - asteroid:earth - asteroid:moon - asteroid:asteroid - asteroid:hydrogen atom

The following five diagrams show pairs of astronomical objects that are all separated by the same distance d. Assume the asteroids are all identical and relatively small, just a few kilometers across. Considering only the two objects shown in each pair, rank the strength, from strongest to weakest, of the gravitational force acting on the asteroid on the left.

- asteroid:sun - asteroid:earth - asteroid:moon - asteroid:asteroid - asteroid:hydrogen atom

How does the brightness of light on a surface change when a point source of light is six times as far away? Express your answer using three significant figures.

1/36

When the pumpkin is shot straight upward with an initial speed of 14 m/s, what is the maximum height above its initial location? Express your answer with appropriate units.

10 m

First, you will investigate purely vertical motion. The kinematics equation for vertical motion (ignoring air resistance) is given by y(t)=y0+v0t−(1/2)gt2, where y0=0 is the initial position, v0 is the initial speed, and g is the acceleration due to gravity. Drag the cannon downwards so it is at ground level, or 0 mm (which represents the initial height of the object), then fire the pumpkin straight upward (at an angle of 90∘90∘) with an initial speed of 14 m/s. How long does it take for the pumpkin to hit the ground? Express your answer with the appropriate units.

2.8 s

Now, let's see what happens when the cannon is high above the ground. Click on the cannon, and drag it upward as far as it goes (15 mm above the ground). Set the initial velocity to 14 m/sm/s, and fire several pumpkins while varying the angle. For what angle is the range the greatest?

30

Erase all the trajectories, and fire the pumpkin vertically again with an initial speed of 14 m/sm/s. As you found earlier, the maximum height is 9.99 mm. If the pumpkin isn't fired vertically, but at an angle less than 90∘90∘, it can reach the same maximum height if its initial speed is faster. Set the initial speed to 22 m/sm/s, and find the angle such that the maximum height is roughly the same. Experiment by firing the pumpkin with many different angles. What is this angle?

40

The range is the horizontal distance from the cannon when the pumpkin hits the ground. This distance is given by the product of the horizontal velocity (which is constant) and the amount of time the pumpkin is in the air (which is determined by the vertical component of the initial velocity, as you just discovered). Set the initial speed to 14 m/sm/s, and fire the pumpkin several times while varying the angle between the cannon and the horizontal. For which angle is the range a maximum (with the initial speed held constant)?

45

Find the areas that would be illuminated if the wall were moved to distances of 3.0 mm, 7.0 mm, and 12 mm from the source. Express your answers in squared meters separated by commas.

9,49,140

What is the magnitude of the gravitational force between Earth and a 1-kg body on its surface?

9.8 N

By what factor would your weight change if Earth's diameter were decreased by the factor of 5 and its mass were decreased by the factor of 5? Express your answer using two significant figures.

????

Rank KEs from greatest to least. Rank from greatest to least. To rank items as equivalent, overlap them.

A B C D

Rank accelerations from greatest to least. Rank from greatest to least. To rank items as equivalent, overlap them

A B C D

Rank gravitational forces from greatest to least. Rank from greatest to least. To rank items as equivalent, overlap them.

A B C D

Rank momenta from greatest to least. Rank from greatest to least. To rank items as equivalent, overlap them.

A B C D

Rank speeds from greatest to least. Rank from greatest to least. To rank items as equivalent, overlap them.

A B C D

Rank total energies (KEs + PEs) from greatest to least. Rank from greatest to least. To rank items as equivalent, overlap them.

A=B=C=D

Rank from greatest to least their orbital speeds. Rank from greatest to least. To rank items as equivalent, overlap them.

ABC

The ______ of an object is a measure of the amount of matter it contains. On the other hand______is a measure of gravitational force on an object.

mass, weight

The crew of a cargo plane wishes to drop a crate of supplies on a target below. To hit the target, when should the crew drop the crate? Ignore air resistance.

Before the plane is directly over the target

When Dr. Hewitt releases the two projectiles, which one hits the ground first?

Both balls hit the ground at the same time.

Rank PEs from greatest to least. Rank from greatest to least. To rank items as equivalent, overlap them.

D C B A

What is Newton's law of gravitation?

Every body in the universe attracts every other body with a mutually attracting force. For two bodies, this force is directly proportional to the product of their masses and inversely proportional to the square of the distance separating them.

What is the expression for a gravitational force? Assume that m1 and m2 are the masses, d is the distance between their centers, G is the universal constant of gravitation. Express your answer in terms of some or all of the variables m1, m2, d and the universal constant of gravitation G.

F= Gm(bottom) 1 m(bottom) 2/ d2

Why do the two objects hit the table at the relative times that they do?

Gravity pulls the same amount on each ball, and they each drop the same distance

What happens to the trajectory of the cannonball when you increase the diameter while keeping the mass constant?

Increasing the size makes the range of the trajectory decrease.

When you whirl a can at the end of a string in a circular path, what is the direction of the force that acts on the can? Neglect the downward pull of gravity.

The force is directed toward the center of the circle.

Why does the gravity in the Space Shuttle compare with the gravity on Earth the way it does?

The Space Shuttle and the surface of the Earth are about the same distance from the center of the Earth

Why do the astronauts in the Space Shuttle float around?

The Space Shuttle is in free fall, so the shuttle and the astronauts inside it are continuously falling toward the Earth. They thus experience apparent weightlessness.

Which ball (if either) has the greatest speed at the moment of impact?

The ball thrown horizontally

Consider the video demonstration that you just watched. A more complete explanation of what you saw will be possible after covering Newton's laws. For now, consider the following question: How would the result of this experiment change if we replaced the ball with another one that had half the mass? Ignore air resistance.

The ball would still land in the cart.

Assume that you weight yourself on a bathroom scale. Would the springs inside a bathroom scale be more compressed or less compressed if you weighed yourself in an elevator that was moving downward at constant velocity?

The compression of the springs would be unchanged

Assume that you weight yourself on a bathroom scale. Would the springs inside a bathroom scale be more compressed or less compressed if you weighed yourself in an elevator that was moving upward at constant velocity?

The compression of the springs would be unchanged.

What is the effect of air drag on the height and range of batted baseballs?

The effect of air drag is that both range and height are decreased.

As you found in Part A, your weight will be greater than normal when the elevator is moving upward with increasing speed. For what other motion would your weight also be greater than your normal weight?

The elevator moves downward while slowing in speed.

How does the gravity in the Space Shuttle compare with the gravity on Earth's surface?

The gravity in the Space Shuttle is approximately equal to the gravity on the surface of the Earth.

With no air drag, what happens to the horizontal component for the ball?

The horizontal component of the ball's velocity remains the same.

If the initial speed of the pumpkin is doubled, how does the maximum height change? (Note: for this part, as well as later parts, you will need to use the zoom in and out buttons to see the full trajectories)

The maximum height increases by a factor of four.

Which projectile spends more time in the air, the one fired from 30∘∘ or the one fired from 60∘∘?

The one fired from 60∘

How does the range of the pumpkin change if its initial velocity is tripled (keeping the angle fixed and less than 90∘90∘)?

The pumpkin's range is nine times as far.

You might think that it is never a good approximation to ignore air resistance. However, often it is. Fire the cannonball without air resistance, and then fire it with air resistance (same angle and initial speed). Then, adjust the mass of the cannonball (increase it and decrease it) and see what happens to the trajectory. Don't change the diameter. When does the range with air resistance approach the range without air resistance?

The range with air resistance approaches the range without air resistance as the mass of the cannonball is increased.

Assume that you weight yourself on a bathroom scale. Would the springs inside a bathroom scale be more compressed or less compressed if you weighed yourself in an elevator that was accelerating downward?

The springs would be less compressed.

Assume that you weight yourself on a bathroom scale. Would the springs inside a bathroom scale be more compressed or less compressed if you weighed yourself in an elevator that was accelerating upward?

The springs would be more compressed.

So far in this tutorial, you have been launching a pumpkin. Let's see what happens to the trajectory if you launch something bigger and heavier, like a car. Compare the trajectory and range of the pumpkin to that of the car, using the same initial speed and angle (e.g., 45∘45∘). (Be sure that air resistance is still turned off.) Which statement is true?

The trajectories and thus the range of the car and the pumpkin are identical.

In the previous part, you discovered that the trajectory of an object does not depend on the object's size or mass. But if you have ever seen a parachutist or a feather falling, you know this isn't really true. That is because we have been neglecting air resistance, and we will now study its effects here. For the following parts, select the "Lab" mode of the simulation found at the bottom of the screen. Notice that you can adjust the mass and diameter of the object being launched. Turn on Air Resistance by checking the box. Fire a cannonball with an initial speed of 18 m/sm/s and an angle of 45∘45∘. Compare the trajectory to the case without air resistance. How do the trajectories differ?

The trajectory with air resistance has a shorter range.

What happens to the vertical component of its velocity as the ball rises?

The vertical component of the ball's velocity decreases.

The figure shows two trajectories, made by two pumpkins launched with different angles and possibly different initial speeds. Based on the figure, for which trajectory was the pumpkin in the air for the greatest amount of time?

Trajectory A

Which depends on gravity - weight or mass?

Weight depends on gravity

When is your weight equal to mg?

When you are in a state of zero acceleration on the Earth's surface.

When is your weight greater than mg?

When you are in an elevator that accelerates upward near the Earth's surface.

When is your weight zero?

When you are in free fall.

Is it possible to simulate weight in a space habitat?

Yes, weight can be simulated with the centripetal force acting on a person moving in a circular path.

Consider the video you just watched. Suppose we replace the original launcher with one that fires the ball upward at twice the speed. We make no other changes. How far behind the cart will the ball land, compared to the distance in the original experiment?

four times as far

Suppose you are in an elevator. As the elevator starts upward, its speed will increase. During this time when the elevator is moving upward with increasing speed, your weight will be __________.

greater than your normal weight at rest

Suppose you are in an elevator that is moving upward. As the elevator nears the floor at which you will get off, its speed slows down. During this time when the elevator is moving upward with decreasing speed, your weight will be __________.

less than your normal weight at rest

Consider Earth and the Moon. As you should now realize, the gravitational force that Earth exerts on the Moon is equal and opposite to that which the Moon exerts on Earth. Therefore, according to Newton's second law of motion __________.

the Moon has a larger acceleration than Earth, because it has a smaller mass

If you are standing on a scale in an elevator, what exactly does the scale measure?

the force you exert on the scale

Is it correct to say that the planets of the solar system are simply projectiles falling around the Sun?

yes