Online PHYS 1011K Physical Science - Chapter 4 Homework

Ranking Task: Gravity and Newton's Laws Part C 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 : steroid - asteroid : hydrogen atom According to Newton's second law, the asteroid with the largest acceleration will be the one that has the strongest gravitational force exerted on it by the object on the right. That is why the ranking here is the same as the ranking for Part A.

Ranking Task: Gravity and Newton's Laws Part A The following five diagrams show pairs of astronomical objects that are all separated by the same distance dd. 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 : steroid - asteroid : hydrogen atom Because the distance is the same for all five cases, the gravitational force depends only on the product of the masses. And because the same asteroid is on the left in all five cases, the relative strength of gravitational force depends on the mass of the object on the right. Continue to Part B to explore what happens if we instead ask about the gravitational force acting on the object on the right.

Ranking Task: Gravity and Newton's Laws Part B 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 : steroid - asteroid : hydrogen atom Newton's third law tells us that the gravitational force exerted on the asteroid on the left by the object on the right will be exactly the same as the gravitational force exerted on the object on the right by the asteroid on the left. That is why the ranking here is the same as the ranking for Part A.

PhET Tutorial: Projectile Motion Part D Erase all the trajectories, and fire the pumpkin vertically again with an initial speed of 14 m/s. As you found earlier, the maximum height is 9.99 m. If the pumpkin isn't fired vertically, but at an angle less than 90∘, it can reach the same maximum height if its initial speed is faster. Set the initial speed to 22 m/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? 35∘ 40∘ 45∘ 50∘ 55∘

40∘ Notice that the initial speed in the vertical direction is given by (22 m/s)sin(40∘)=14 m/s. The pumpkin launched at this angle reaches the same height as the vertically launched pumpkin because they have the same initial speeds in the vertical direction.

Think and Solve 4.49 An airplane is flying horizontally with speed 1100 km/h (310 m/s) when an engine falls off. Neglecting air resistance, assume it takes 31 s for the engine to hit the ground. Part A Find the altitude of the airplane. (Use g=9.8m/s2.). Express your answer to two significant figures and include the appropriate units.

4700 m

Multiple Choice Question 4.5.13 Part A A stone is thrown horizontally from the top of a cliff. One second after leaving your hand it drops a vertical distance of 15 m. 5 m. 10 m.

5 m

Think and Solve 4.49 An airplane is flying horizontally with speed 1100 km/h (310 m/s) when an engine falls off. Neglecting air resistance, assume it takes 31 s for the engine to hit the ground. Part B Find the horizontal distance the airplane engine falls. Express your answer to two significant figures and include the appropriate units.

9600 m

Multiple Choice Question 4.5.19 Part A A bullet fired horizontally hits the ground in 0.5 s. If it had been fired with twice the velocity it would have hit the ground in more than 0.5 s. less than 0.5 s. 0.5 s.

A bullet fired horizontally hits the ground in 0.5 s. If it had been fired with twice the velocity it would have hit the ground in 0.5 s.

Reading Check 4.18 Part A A projectile is launched upward at an angle of 75∘ from the horizontal and strikes the ground a certain distance downrange. For what other angle of launch at the same speed would this projectile land just as far away? 15∘ 30∘ 60∘ 45∘

A projectile is launched upward at an angle of 75∘ from the horizontal and strikes the ground a certain distance downrange. For what other angle of launch at the same speed would this projectile land just as far away? 15∘

Prelecture Reading Question 4.9 Part A A satellite in elliptical orbit about Earth travels fastest when it moves _______. far from Earth close to Earth anywhere in its orbit (speed is the same everywhere) between the near and far points from Earth

A satellite in elliptical orbit about Earth travels fastest when it moves close to Earth.

Think and Rank 4.60 The dashed lines show three circular orbits about Earth.(Figure 1) Part A Rank from greatest to least their orbital speeds. Rank from greatest to least. To rank items as equivalent, overlap them.

A, B, C

Think and Rank 4.61 The positions of a satellite in elliptical orbit are indicated.(Figure 1) Part A Rank gravitational forces from greatest to least. Rank from greatest to least. To rank items as equivalent, overlap them.

A, B, C, D

Think and Rank 4.61 The positions of a satellite in elliptical orbit are indicated.(Figure 1) Part B Rank speeds from greatest to least. Rank from greatest to least. To rank items as equivalent, overlap them.

A, B, C, D

Think and Rank 4.61 The positions of a satellite in elliptical orbit are indicated.(Figure 1) Part C Rank momenta from greatest to least. Rank from greatest to least. To rank items as equivalent, overlap them.

A, B, C, D

Think and Rank 4.61 The positions of a satellite in elliptical orbit are indicated.(Figure 1) Part D Rank KEs from greatest to least. Rank from greatest to least. To rank items as equivalent, overlap them.

A, B, C, D

Think and Rank 4.61 The positions of a satellite in elliptical orbit are indicated.(Figure 1) Part G Rank accelerations from greatest to least. Rank from greatest to least. To rank items as equivalent, overlap them.

A,B,C,D

Think and Rank 4.61 The positions of a satellite in elliptical orbit are indicated.(Figure 1) Part F 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 (all equal in middle)

Visual Activity: Exploring a Person's Weight in a Moving Elevator Part C 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 upward with constant velocity. The elevator moves downward with constant velocity. The elevator moves upward while slowing in speed. The elevator moves downward while slowing in speed. The elevator moves downward while increasing in speed.

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. When the elevator is moving downward, a downward acceleration would mean an increasing downward speed. Therefore, as your answer correctly states, an upward acceleration would mean a decreasing downward speed.

PhET Tutorial: Projectile Motion Part F 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? The pumpkins are in the air for the same amount of time. It's impossible to tell solely based on the figure. Trajectory A Trajectory B

Based on the figure, for which trajectory was the pumpkin in the air for the greatest amount of time? Trajectory A All that matters is the vertical height of the trajectory, which is based on the component of the initial velocity in the vertical direction (v0 sinθ). The higher the trajectory, the more time the pumpkin will be in the air, regardless of the pumpkin's range or horizontal velocity.

Video Tutor: Ball Fired Upward from Moving Cart First, launch the video below. You will be asked to use your knowledge of physics to predict the outcome of an experiment. Then, close the video window and answer the questions at right. You can watch the video again at any point. Part A 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. After the plane has flown over the target Before the plane is directly over the target When the plane is directly over the target

Before the plane is directly over the target At the moment it is released, the crate shares the plane's horizontal velocity. In the absence of air resistance, the crate would remain directly below the plane as it fell.

Video: Projectile Motion Part A When Dr. Hewitt releases the two projectiles, which one hits the ground first? The ball that drops vertically hits the ground first. Both balls hit the ground at the same time. The ball that goes horizontally hits the ground first.

Both balls hit the ground at the same time. As pointed out in the movie, the easiest way to tell that the balls hit at the same time is by listening to the sounds they make when hitting. In this particular movie, you can also see that the balls hit at the same time.

Think and Rank 4.60 The dashed lines show three circular orbits about Earth.(Figure 1) Part B Rank from greatest to least their their time to orbit Earth.. Rank from greatest to least. To rank items as equivalent, overlap them.

C, B, A

Think and Rank 4.61 The positions of a satellite in elliptical orbit are indicated.(Figure 1) Part E Rank PEs from greatest to least. Rank from greatest to least. To rank items as equivalent, overlap them.

D, C, B, A

PhET Tutorial: Projectile Motion Part I 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/s, and fire several pumpkins while varying the angle. For what angle is the range the greatest? 45∘ 30∘ 50∘ 20∘ 40∘

For what angle is the range the greatest? 30∘ Since the cannon is very high off the ground, the pumpkin will be in the air for an appreciable amount of time even if the pumpkin is launched nearly horizontally. Thus, the amount of time the pumpkin is in the air isn't proportional to the vertical component of the initial velocity (as it was when the cannon was on the ground). This means that the initial horizontal velocity is more important, resulting in an optimal angle less than 45∘. You should realize that the range equation given in Part H, R=2v02sin(θ)cos(θ)/g, is not valid when the initial height is not zero. You can also verify that, if you change the initial velocity, the optimal angle also changes!

PhET Tutorial: Projectile Motion Part G 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)? 0∘ 90∘ 60∘ 30∘ 45∘

For which angle is the range a maximum (with the initial speed held constant)? 45∘ When the pumpkin is launched near a level ground, 45∘ is the optimum angle. If launched with a greater angle, it stays in the air longer, but its horizontal speed is slower, and it won't go as far. If launched with a smaller angle, its horizontal speed is faster, but it won't stay in the air as long and it won't go as far. The product between the horizontal speed and the amount of time in the air is largest when the angle is 45∘.

Video: Projectile Motion Part B Why do the two objects hit the table at the relative times that they do? The inertia of the ball that is shot horizontally makes it less susceptible to gravity. Gravity pulls the same amount on each ball, and they each drop the same distance. The ball that is shot horizontally travels a longer path in the air.

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

Think and Rank 4.56 Part A The planet and its moon gravitationally attract each other. Rank the forces of attraction between each pair from greatest to least.(Figure 1) Rank from greatest to least. To rank items as equivalent, overlap them. A. M=D=M B.2m-D-m C.M-D-2m D.M=2D=2m

Greatest B & C A D Least

PhET Tutorial: Projectile Motion Part K 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/s and an angle of 45∘. Compare the trajectory to the case without air resistance. How do the trajectories differ? The trajectories are identical. The trajectory with air resistance has a shorter range. The trajectory with air resistance has a longer range.

How do the trajectories differ? The trajectory with air resistance has a shorter range. Air resistance is a force due to the object ramming through the air molecules, and is always in the opposite direction to the object's velocity. This means the air resistance force will slow the object down, resulting in a shorter range (the simulation assumes the air is still; there is no strong tailwind).

PhET Tutorial: Projectile Motion Part H How does the range of the pumpkin change if its initial velocity is tripled (keeping the angle fixed and less than 90∘)? The pumpkin's range is eighteen times as far. The pumpkin's range is three times as far. The pumpkin's range is nine times as far.

How does the range of the pumpkin change if its initial velocity is tripled (keeping the angle fixed and less than 90∘)? The pumpkin's range is nine times as far. Since the vertical component of the velocity is three times as large, it takes three times as long to hit the ground. The horizontal component of the velocity is also tripled, and since the range is equal to the horizontal velocity times the amount of time the pumpkin is in the air, the range increases by a factor of nine. The results of this question and the previous question can be summarized by the range equation, which is R=2v02sin(θ)cos(θ)/g.

Video Tutor: Ball Fired Upward from Accelerating Cart Part A 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? the same distance four times as far twice as far half as far by a factor not listed above

How far behind the cart will the ball land, compared to the distance in the original experiment? four times as far The ball will spend twice as much time in the air t=2v0y/g, where v0y is the ball's initial upward velocity). When subtracting the horizontal distance the cart travels in time,t, from the horizontal distance the ball travels in time,t, the term involving initial velocity of the cart (which is also the horizontal velocity of the ball) cancels out, leaving only d=12 axt2d=12 axt2 (where ax is the cart's horizontal acceleration). The ball will land four times further behind.

PhET Tutorial: Projectile Motion Part C 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 1.4 (square root of 2). The maximum height increases by a factor of four. The maximum height increases by a factor of two.

If the initial speed of the pumpkin is doubled, how does the maximum height change? The maximum height increases by a factor of four. Since the amount of time it takes to reach the maximum height doubles, and since its average velocity in going upward also doubles (the average velocity is equal to half the initial velocity), the height it reaches before stopping increases by a factor of four (distance is equal to the average velocity multiplied by the time duration).

Visual Activity: Exploring a Person's Weight in a Moving Elevator Part C If you are standing on a scale in an elevator, what exactly does the scale measure? your mass the force you exert on the scale he gravitational force exerted on you by Earth

If you are standing on a scale in an elevator, what exactly does the scale measure? the force you exert on the scale You probably recognize that neither your mass nor the gravitational force exerted on you change when you are in an elevator. The scale measures the force that is exerted on it, which in an elevator is a combination of the force due to your normal weight and a force due to the elevator's acceleration.

Visual Activity: Exploring a Person's Weight in a Moving Elevator Part B 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 __________. greater than your normal weight at rest equal to your normal weight at rest less 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. Even though the elevator is still moving upward, the fact that its speed is slowing means that the acceleration is downward; the situation is rather like that of a ball that is still on its way up after you throw it, even though it is being pulled downward with the acceleration of gravity. Because the acceleration of the elevator is downward, your weight is lower than normal.

Visual Activity: Exploring a Person's Weight in a Moving Elevator First, launch the application below. Explore the animation to help you with the following set of questions. Notice that when the elevator is stationary, we see the person's "normal weight" (weight at rest) of 140 lbs. Click other buttons to see what happens to the person's weight when the elevator is moving. Part A 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 equal to your normal weight at rest less than your normal weight at rest

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. Increasing speed means acceleration, and when the elevator is accelerating upward you will feel a force pressing you to the floor, making your weight greater than your normal (at rest) weight.

Video Tutor: Dropped and Thrown Balls First, launch the video below. You will be asked to use your knowledge of physics to predict the outcome of an experiment. Then, close the video window and answer the questions at right. You can watch the video again at any point. Part A Which ball (if either) has the greatest speed at the moment of impact? The ball thrown horizontally The dropped ball Both balls have the same speed.

The ball thrown horizontally. The two balls have the same vertical velocity when they land, but the thrown ball has an additional horizontal velocity component. Since speed is defined as the magnitude of the resultant velocity vector, the thrown ball is moving faster when it lands.

Video Tutor: Ball Fired from Cart on Incline First, launch the video below. You will be asked to use your knowledge of physics to predict the outcome of an experiment. Then, close the video window and answer the questions at right. You can watch the video again at any point. Part A 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 land ahead of the cart. The ball would land behind the cart. The ball would still land in the cart.

The ball would still land in the cart.

Think and Solve 4.49 An airplane is flying horizontally with speed 1100 km/h (310 m/s) when an engine falls off. Neglecting air resistance, assume it takes 31 s for the engine to hit the ground. Part C If the airplane somehow continues to fly as if nothing had happened, where is the engine relative to the airplane at the moment the engine hits the ground? The engine is directly below the airplane. The engine is before the airplane. The engine is behind the airplane.

The engine is directly below the airplane.

Think and Solve 4.46 Consider a pair of planets for which the distance between them is decreased by a factor of 4. Part A How many times does the force between them increase? Express your answer as an integer.

The force between the planets increases by a factor of 16. .

Plug and Chug 4.37 F=Gm1m2d2 Part A Calculate the force of gravity on the 1.5-kg mass if it were 1.3×107 mm above Earth's surface (that is, if it were three Earth radii from Earth's center). Express your answer to two significant figures and include the appropriate units.

The force of gravity on the 1.5-kg mass is 1.6 N.

PhET Tutorial: Projectile Motion Part L 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. The size of the object doesn't affect the trajectory. Increasing the size makes the range of the trajectory increase.

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. Since the surface area increases if the diameter increases, the object is sweeping through more air, causing more collisions, and a greater force of air drag (in fact, if the diameter is doubled, for a given speed, the force of air drag is increased by a factor of four). This greater force of air drag causes the object to slow down more quickly, resulting in a slower average speed and a shorter range.

Multiple Choice Question 4.5.32 Part A A softball player determines her pitching speed by throwing a ball horizontally from an elevation of 5 m above the ground. The ball lands 20 m downrange. What is her pitching speed? 25 m/s 10 m/s 20 m/s 5 m/s none of the above

What is her pitching speed? 20 m/s

PhET Tutorial: Projectile Motion Part M 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. The range with air resistance approaches the range without air resistance as the mass of the cannonball is decreased. It never does. Regardless of the mass, the range with air resistance is always shorter than the range without.

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. As the mass is increased, the force of gravity on the cannonball becomes larger. The force due to air drag just depends on the speed and the size of the object, so it doesn't change if the mass changes. As the mass gets large enough, the force of gravity becomes much larger than the air drag force in the vertical direction, and so the air drag force becomes negligible. This results in a trajectory nearly the same as when air resistance is turned off. Thus, for small, dense objects (like rocks and bowling balls), air resistance is typically unimportant, but for objects with a low density (like feathers) or a very large surface area (like parachutists), air resistance is very important.

Video Tutor: Range of a Gun at Two Firing Angles Part A Which projectile spends more time in the air, the one fired from 30∘ or the one fired from 60∘? The one fired from 60∘ They both spend the same amount of time in the air. The one fired from 30∘

Which projectile spends more time in the air, the one fired from 30∘ or the one fired from 60∘? The one fired from 60∘ The projectile fired from 60∘ has a greater vertical velocity than the one fired from 30∘, so it spends more time in the air.

PhET Tutorial: Projectile Motion Part E In the previous part, you found that a pumpkin fired with an initial speed of 22 m/s and an angle of 40∘ reaches the same height as a pumpkin fired vertically with an initial speed of 14 m/s. Which pumpkin takes longer to land? The pumpkin fired vertically stays in the air longer. Both pumpkins are in the air the same amount of time. The pumpkin fired at an angle of 40∘ stays in the air longer.

Which pumpkin takes longer to land? Both pumpkins are in the air the same amount of time. The vertical component of the velocity determines how long the pumpkin will be in the air (and its maximum height). The horizontal component of the pumpkin's velocity does not affect this hang time.

PhET Tutorial: Projectile Motion Part J 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∘). (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. The trajectories differ; the range of the car is longer than that of the pumpkin. The trajectories differ; the range of the car is shorter than that of the pumpkin.

Which statement is true? The trajectories and thus the range of the car and the pumpkin are identical. Since we are ignoring air resistance, the trajectory of the object does not depend on its mass or size. In the next part, you will turn on air resistance and discover what changes.

PhET Tutorial: Projectile Motion Part B 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.

Your answer 10m was either rounded differently or used a different number of significant figures than required for this part. Notice that this value could be determined from the kinematics equation. Since you found it takes 2.85 ss for the pumpkin to reach the ground, it must take 1.43 ss to reach the maximum height, which gives y(t=1.43s)=(14m/s)(1.43s)−(1/2)(9.8m/s2)(1.43s)2=10my(t=1.43s)=(14m/s)(1.43s)−(1/2)(9.8m/s2)(1.43s)2=10m.

Extra 4.01 Part A A hypothetical planet has a radius 2.1 times that of Earth, but has the same mass. What is the acceleration due to gravity near its surface? Express your answer to two significant figures and include the appropriate units.

Your answer 2.22ms2 was either rounded differently or used a different number of significant figures than required for this part.

PhET Tutorial: Projectile Motion Part A 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∘) 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.

Your answer 2.86s was either rounded differently or used a different number of significant figures than required for this part. Notice that this value could be determined from the kinematics equation. Given that the initial and final height of the pumpkin is 0 mm, the kinematics equation becomes (v0−0.5gt)=0, or t=2v0/g=2.9 s. This calculation is interesting because it shows that, for vertical motion, the time the pumpkin is in the air is proportional to its initial speed.

Plug and Chug 4.39 F=Gm1m2d2 Part A Find the force of gravity between Earth (mass=6.0×1024kg) and the Sun (mass=2.0×1030kg).(The average Earth-Sun distance is 1.5×1011m.) Express your answer to two significant figures and include the appropriate units.

Your answer 3.6⋅1022N was either rounded differently or used a different number of significant figures than required for this part.

Reading Check 4.26 Part A Is the period longer or shorter for orbits of greater altitude? shorter The period goes to zero as altitude increases. longer the same

longer

Prelecture Reading Question 4.3 Consider a space probe three times as far from Earth's center as it would be at Earth's surface. Compared to at Earth's surface, its gravitational attraction to Earth at this distance is about _______. one-half as much one-ninth as much zero one-third as much

one-ninth as much

Ranking Task: Gravity and Newton's Laws Part D 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 Earth has a larger acceleration than the Moon, because it has a larger mass the Moon and Earth both have equal accelerations, because the forces are equal

the Moon has a larger acceleration than Earth, because it has a smaller mass. Newton's second law of motion, F=ma, means that for a particular force F, the product mass x acceleration must always be the same. Therefore if mass is larger, acceleration must be smaller, and vice versa.

Reading Check 4.8 Part A Would the springs inside a bathroom scale be more compressed or less compressed if you weighed yourself in an elevator that accelerated upward? Accelerated downward? upward, less compressed; downward, less compressed upward, more compressed; downward, less compressed upward, more compressed; downward, more compressed upward, less compressed; downward, more compressed

upward, more compressed; downward, less compressed

Reading Check 4.9 Part A Would the springs inside a bathroom scale be more compressed or less compressed if you weighed yourself in an elevator that moved upward at constant velocity? What about in an elevator that moved downward at constant velocity? upward, more compressed; downward, less compressed upward, more compressed; downward, no change upward, no change; downward, no change. upward, less compressed; downward, more compressed

upward, no change; downward, no change.