Physics Fall Final Exam

Suppose a spacecraft orbits the moon in a very low, circular orbit, just a few hundred meters above the lunar surface. The moon has a diameter of 3500 km, and the free-fall acceleration at the surface is 1.60 m/s2. How fast is this spacecraft moving?

1700 m/s

There are competitions in which pilots fly small planes low over the ground and drop weights, trying to hit a target. A pilot flying low and slow drops a weight; it takes 2.4 s to hit the ground, during which it travels a horizontal distance of 100 m . Now the pilot does a run at the same height but twice the speed. How much time does it take the weight to hit the ground?

2.4 s

Suppose one night the radius of the earth doubled but its mass stayed the same. What would be an approximate new value for the free-fall acceleration at the surface of the earth?

2.5 m/s2

A newly discovered planet has twice the mass and three times the radius of the earth. What is the free-fall acceleration at its surface, in terms of the free-fall acceleration g at the surface of the earth?

2/9g

There are competitions in which pilots fly small planes low over the ground and drop weights, trying to hit a target. How far does it travel before it lands?

200 m

While standing in a low tunnel, you raise your arms and push against the ceiling with a force of 200 N. Your mass is 70 kg. What force does the ceiling exert on you?

200N

A ball on a string moves around a complete circle, once a second, on a frictionless, horizontal table. The tension in the string is measured to be 6.0 N . What would the tension be if the ball went around in only half a second?

24 N

The cylindrical space station in the Figure, d = 290 m in diameter, rotates in order to provide artificial gravity of g for the occupants. How much time does the station take to complete one rotation?

24 s

Two cylindrical space stations, the second four times the diameter of the first, rotate so as to provide the same amount of artificial gravity. If the first station makes one rotation in the time T, then the second station makes one rotation in what time?

2T

A football is kicked at an angle of 35° with a speed of 24 m/s . To the nearest second, how long will the ball stay in the air?

3 s

A 3.5 kg dog sits on the floor of an elevator that is accelerating downward at 1.20 m/s2. What is the magnitude of the normal force of the elevator floor on the dog?

30 N

Wings on race cars push them into the track. The increased normal force makes large friction forces possible. At one Formula One racetrack, cars turn around a half-circle with diameter 190 m at 68 m/s. For a 610 kg vehicle, the approximate minimum static friction force to complete this turn is

30000 N

A 6.0 kg block has an acceleration of 0.50 m/s2 when a force is exerted on it. A second block has an acceleration of 0.10 m/s2 when subject to the same force. What is the mass of the second block?

30kg

A 2.5 kg ball is suspended by two light strings as shown in the Figure. What is the tension T in the angled string?

32 N

A car drives horizontally off a 83-m-high cliff at a speed of 19 m/s . Ignore air resistance. How long will it take the car to hit the ground?

4.1 s

A cannon, elevated at 40∘ is fired at a wall 300 m away on level ground, as shown in the figure below. The initial speed of the cannonball is 89 m/s. How long does it take for the ball to hit the wall?

4.4 s

If you kick a football, at what angle to the ground should you kick the ball for the maximum range - that is, the greatest distance down the field?

45

A football is kicked at an angle of 35 ∘ with a speed of 24 m/s . How far will the ball travel?

55 m

Formula One race cars are capable of remarkable accelerations when speeding up, slowing down, and turning corners. At one track, cars round a corner that is a segment of a circle of radius 95 m at a speed of 68 m/s. What is the approximate magnitude of the centripetal acceleration, in units of g?

5g

A car drives horizontally off a 83-m-high cliff at a speed of 19 m/s . Ignore air resistance. How far from the base of the cliff will the car hit?

78 m

Suppose you and a friend, each of mass 50 kg , go to the park and get on a 4.0-m-diameter merry-go-round. You stand on the outside edge of the merry-go-round, while your friend pushes so that it rotates once every 7.0 seconds. What is the magnitude of the (apparent) outward force that you feel?

81 N

While standing in a low tunnel, you raise your arms and push against the ceiling with a force of 200 N. Your mass is 70 kg. What force does the floor exert on you?

890N

A ball is fired from a cannon at point 1 and follows the trajectory shown in the Figure. Air resistance may be neglected. Five possible vectors are also shown in the figure; the letter E represents the zero vector. Which vector best represents the ball's acceleration at position 2?

A

A ball is fired from a cannon at point 1 and follows the trajectory shown in the Figure. Air resistance may be neglected. Five possible vectors are also shown in the figure; the letter E represents the zero vector. Which vector best represents the ball's acceleration at position 3?

A

A car travels at constant speed along the curved path shown in the Figure. Five possible vectors are also shown in the figure; the letter E represents the zero vector. Which vector best represents the car's acceleration at point 3?

A

Two vectors appear as in the figure. Which combination points directly downward?

-Q - P

Is the object described here in static equilibrium, dynamic equilibrium, or not in equilibrium at all? You're straining to hold a 200 pound barbell over your head.

Static equilibrium

Two planets orbit a star. You can ignore the gravitational interactions between the planets. Planet 1 has orbital radius r1 and planet 2 has r2 = 25 r1. Planet 1 orbits with period T1. Planet 2 orbits with period

T2 = 125T1

Suppose \ou are an astronaut in deep space, far from an\ source of gravit\. You have tZo objects that look identical, but one has a large mass and the other a small mass.

Assuming you can exert a reproducible force in throwing both objects, you could throw each and note the acceleration each obtains..

A car travels at constant speed along the curved path shown in the Figure. Five possible vectors are also shown in the figure; the letter E represents the zero vector. Which vector best represents the car's velocity at position 1?

B

A car travels at constant speed along the curved path shown in the Figure. Five possible vectors are also shown in the figure; the letter E represents the zero vector. Which vector best represents the car's velocity at position 2?

B

A car travels at constant speed along the curved path shown in the Figure. Five possible vectors are also shown in the figure; the letter E represents the zero vector. Which vector best represents the car's velocity at position 3?

B

Which combination of the vectors shown in the Figure has the largest magnitude?

B + A - C

The figure below shows block A sitting on top of block B. A constant force F is exerted on block B, causing block B to accelerate to the right. Block A rides on block B without slipping. Which statement is true?

Block B exerts a friction force on block A, directed to the right.

Dave pushes his four-year-old son Thomas across the snow on a sled. As Dave pushes, Thomas speeds up. Which statement is true?

Both forces have the same magnitude.

A ball is fired from a cannon at point 1 and follows the trajectory shown in the Figure. Air resistance may be neglected. Five possible vectors are also shown in the figure; the letter E represents the zero vector. Which vector best represents the ball's velocity at position 2?

D

A car travels at constant speed along the curved path shown in the Figure. Five possible vectors are also shown in the figure; the letter E represents the zero vector. Which vector best represents the car's acceleration at point 2?

D

Three arrows are shot horizontally. They have left the bow and are traveling parallel to the ground as shown in the figure. Air resistance is negligible. Rank in order, from largest to smallest, the magnitudes of the horizontal forces F1, F2, and F3 acting on the arrows. Some may be equal. State your reasoning.

F1 = F2 = F3 = 0 because there is no change in the horizontal motion of the arrows.

Normally, jet engines push air out the back of the engine, resulting in forward thrust, but commercial aircraft often have thrust reversers that can change the direction of the ejected air, sending it forward. How does this affect the direction of thrust?

If the ejected air is directed forward then thrust force is backward (Newton's 3rd law).

Normally, jet engines push air out the back of the engine, resulting in forward thrust, but commercial aircraft often have thrust reversers that can change the direction of the ejected air, sending it forward. When might these thrust reversers be useful in practice? Select all that apply.

If the ejected air is directed forward then thrust force is backward. This might be desirable to slow the plane down. If the ejected air is directed downward, the thrust force is up. Jets can take off vertically without needing a runway this way.

If you are standing still, the upward normal force on you from the Áoor is equal in magnitude to the weight force that acts on you. But it's possible to move so that the normal force is greater than your weight.

If you jump up, during the initial phase when you are still in contact with the floor, you are accelerating upward. This means the net force on you must be upward, so the upward normal force must be bigger than the downward weight force.

You are going sledding with your friends, sliding down a snowy hill. Friction can't be ignored. Riding solo on your sled, you have a certain acceleration. Would the acceleration change if you let a friend ride with you, increasing the mass?

No, increasing the mass does increase the net force on the system, but it also increases the inertia. a = . Since both the net force and mass are increased they still cancel, leaving the acceleration the same.

Is the object described here in static equilibrium, dynamic equilibrium, or not in equilibrium at all? A girder is lowered into place by a crane. It is slowing down.

Not in equilibrium

Is the object described here in static equilibrium, dynamic equilibrium, or not in equilibrium at all? A rock is falling into the Grand Canyon

Not in equilibrium

The wood block in the figure below is at rest on a wood ramp. In which direction is the static friction force on block 1?

There's not enough information to tell.

If your car is stuck in the mud and you don't have a winch to pull it out, you can use a piece of rope and a tree to do the trick. First, you tie one end of the rope to your car and the other to a tree, then pull as hard as you can on the middle of the rope, as shown in the figure. This technique applies a force to the car much larger than the force that you can apply directly. To see why the car experiences such a large force, look at the forces acting on the center point of the rope, as shown in the figure. The sum of the forces is zero, thus the tension is much greater than the force you apply. It is this tension force that acts on the car and, with luck, pulls it free. When you are pulling on the rope as shown, what is the approximate direction of the tension force on the tree?

West

The Figure shows a situation in which the force of the road on the car's tire points forward. In other situations, the force points backward. Give an example of such a situation.

When the car is going forward and slowing down.

An airplane has been directed to fly in a clockwise circle, as seen from above, at constant speed until another plane has landed. When the plane is going north, is it accelerating?

Yes, it is. Since the plane is moving in a circle and constantly changing direction, at any point along its motion the plane is constantly accelerating.

You are walking up an icy slope. Suddenly your feet slip, and you start to slide backward. Will you slide at a constant speed, or will you accelerate?

You will accelerate because the kinetic friction is less than the maximum static friction.

A block has acceleration a when pulled by a string. If two identical blocks are glued together and pulled with twice the original force, what will their acceleration be?

a

Why is it impossible for an astronaut inside an orbiting space station to go from one end to the other by walking normally?

a. In an orbiting station, after one foot pushes off there isn't a force to bring the astronaut back to the "floor" for the next step.

Walking without slipping requires a static friction force between your feet (or footwear) and the floor. As described in this chapter, the force on your foot as you push off the floor is forward while the force exerted by your foot on the floor is backward. But what about your other foot, the one moved during a stride? What is the direction of the force on that foot as it comes in contact with the floor?

backward

Suppose that, while in a squatting position, you stand on your hands, and then you pull up on your feet with a great deal of force. You are applying a large force to the bottoms of your feet, but no matter how strong you are, you will never be able to lift yourself off the ground. Use your understanding of force and motion to explain why this is not possible.

c. You can't lift yourself off the floor because the net external force on you is still zero.

Give an example of a trip you might take in your car for which the distance traveled as measured on your car's odometer is not equal to the displacement between your initial and final positions.

circular motion with a constant speed

If your car is stuck in the mud and you don't have a winch to pull it out, you can use a piece of rope and a tree to do the trick. First, you tie one end of the rope to your car and the other to a tree, then pull as hard as you can on the middle of the rope, as shown in the figure. This technique applies a force to the car much larger than the force that you can apply directly. To see why the car experiences such a large force, look at the forces acting on the center point of the rope, as shown in the figure. The sum of the forces is zero, thus the tension is much greater than the force you apply. It is this tension force that acts on the car and, with luck, pulls it free. The sum of the three forces acting on the center point of the rope is assumed to be zero because

d. This point is not accelerating.

In an amusement-park ride, cars rolling along at high speed suddenly head up a long, straight ramp. They roll up the ramp, reverse direction at the highest point, then roll backward back down the ramp. Which way does their acceleration vector point as the cars roll back down the ramp?

downward along the ramp

In an amusement-park ride, cars rolling along at high speed suddenly head up a long, straight ramp. They roll up the ramp, reverse direction at the highest point, then roll backward back down the ramp. Which way does their acceleration vector point as the cars roll up the ramp?

downward along the ramp

In an amusement-park ride, cars rolling along at high speed suddenly head up a long, straight ramp. They roll up the ramp, reverse direction at the highest point, then roll backward back down the ramp. Which way does their acceleration vector point at the highest point on the ramp?

downward along the ramp

Scallops use jet propulsion to move from one place to another. Their shells make them denser than water, so they normally rest on the ocean floor. If a scallop wishes to remain stationary, hovering a fixed distance above the ocean floor, it must eject water _____ so that the thrust force on the scallop is _____.

downward, upward

The radius of Jupiter is 11 times that of earth, and the free-fall acceleration near its surface is 2.5 times that on earth. If we someday put a spacecraft in low Jupiter orbit, its orbital speed will be

greater than that for an earth satellite.

A person is pushing horizontally on a box with a constant force, causing it to slide across the floor with a constant speed. If the person suddenly stops pushing on the box, the box will

immediately begin slowing down and eventually stop.

A group of students is making model cars that will be propelled by model rocket engines. These engines provide a nearly constant thrust force. The cars are light-most of the weight comes from the rocket engine-and friction and drag are very small. As the engine fires, it uses fuel, so it is much lighter at the end of the run than at the start. A student ignites the engine in a car, and the car accelerates. As the fuel burns and the car continues to speed up, the magnitude of the acceleration will

increase

Jonathan accelerates away from a stop sign. His eight-year-old daughter sits in the passenger seat. On whom does the back of the seat exert a greater force?

jonathan

Currently, the moon goes around the earth once every 27.3 days. If the moon could be brought into a new circular orbit with a smaller radius, its orbital period would be

less than 27.3 days.

Suppose a spacecraft orbits the moon in a very low, circular orbit, just a few hundred meters above the lunar surface. The moon has a diameter of 3500 km, and the free-fall acceleration at the surface is 1.60 m/s2. The direction of the net force on the craft is

Toward the center of the moon.

Alyssa pushes to the right on a filing cabinet; the friction force from the floor pushes on it to the left. Because the cabinet doesn't move, these forces have the same magnitude. Do they form an action/reaction pair?

no

The floor is frictionless. In which direction is the kinetic friction force on block 2 in the figure?

to the left

The floor is frictionless. In which direction is the kinetic friction force on block 1 in the figure?

to the right

Suppose you are holding a box in front of you and away from your body by squeezing the sides, as shown in the Figure. Choose the correct free-body diagram showing all of the forces on the box.

x direction = equal both sides (n) y direction = downwards + 2 going up (f)

A cannon, elevated at 40∘ is fired at a wall 300 m away on level ground, as shown in the figure below. The initial speed of the cannonball is 89 m/s. At what height h does the ball hit the wall?

160 m

Suppose a spacecraft orbits the moon in a very low, circular orbit, just a few hundred meters above the lunar surface. The moon has a diameter of 3500 km, and the free-fall acceleration at the surface is 1.60 m/s2. How much time does it take for the spacecraft to complete one orbit?

110 min

A 3.5 kg dog sits on the floor of an elevator that is accelerating downward at 1.20 m/s2. What is the magnitude of the force of the dog on the elevator floor?

15 N

A ball thrown at an initial angle of 37.0∘ and initial velocity vi = 20.0 m/s reaches a maximum height h, as shown in the Figure. With what initial speed must a ball be thrown straight up to reach the same maximum height h?

15.1 m/s

A ball is fired from a cannon at point 1 and follows the trajectory shown in the Figure. Air resistance may be neglected. Five possible vectors are also shown in the figure; the letter E represents the zero vector. Which vector best represents the ball's velocity at position 3?

C

A car coasts at a constant speed over a circular hill. Which of the free-body diagrams in the figure is correct?

C

Tennis balls experience a large drag force. A tennis ball is hit so that it goes up and then comes back straight down. The direction of the drag force is

Down and then up.

A person gives a box a shove so that it slides up a ramp, then reverses its motion and slides down. The direction of the force of friction is

Down the ramp and then up the ramp.

Is the object described here in static equilibrium, dynamic equilibrium, or not in equilibrium at all? A box in the back of a truck doesn't slide as the truck stops.

Dynamic equilibrium

Is the object described here in static equilibrium, dynamic equilibrium, or not in equilibrium at all? A girder is lifted at a constant speed by a crane.

Dynamic equilibrium

Is the object described here in static equilibrium, dynamic equilibrium, or not in equilibrium at all? A jet plane has reached its cruising speed and altitude.

Dynamic equilibrium

A car travels at constant speed along the curved path shown in the Figure. Five possible vectors are also shown in the figure; the letter E represents the zero vector. Which vector best represents the car's acceleration at point 1?

E

As seen from above, a car rounds the curved path shown the figure below at a constant speed. Which vector best represents the net force acting on the car?

E

If your car is stuck in the mud and you don't have a winch to pull it out, you can use a piece of rope and a tree to do the trick. First, you tie one end of the rope to your car and the other to a tree, then pull as hard as you can on the middle of the rope, as shown in the figure. This technique applies a force to the car much larger than the force that you can apply directly. To see why the car experiences such a large force, look at the forces acting on the center point of the rope, as shown in the figure. The sum of the forces is zero, thus the tension is much greater than the force you apply. It is this tension force that acts on the car and, with luck, pulls it free. Assume that you are pulling on the rope but the car is not moving. What is the approximate direction of the force of the mud on the car?

East

If your car is stuck in the mud and you don't have a winch to pull it out, you can use a piece of rope and a tree to do the trick. First, you tie one end of the rope to your car and the other to a tree, then pull as hard as you can on the middle of the rope, as shown in the figure. This technique applies a force to the car much larger than the force that you can apply directly. To see why the car experiences such a large force, look at the forces acting on the center point of the rope, as shown in the figure. The sum of the forces is zero, thus the tension is much greater than the force you apply. It is this tension force that acts on the car and, with luck, pulls it free. Suppose your efforts work, and the car begins to move forward out of the mud. As it does so, the force of the car on the rope is

Equal to the force of the rope on the car.

Suppose a spacecraft orbits the moon in a very low, circular orbit, just a few hundred meters above the lunar surface. The moon has a diameter of 3500 km, and the free-fall acceleration at the surface is 1.60 m/s2. The material that comprises the side of the moon facing the earth is actually slightly more dense than the material on the far side. When the spacecraft is above a more dense area of the surface, the moon's gravitational force on the craft is a bit stronger. In order to stay in a circular orbit of constant height and speed, the spacecraft could fire its rockets while passing over the denser area. The rockets should be fired so as to generate a force on the craft

Opposite the direction of motion.

Josh and Taylor, standing face-to-face on frictionless ice, push off each other, causing each to slide backward. Josh is much bigger than Taylor. After the push, which of the two is moving faster?

Taylor will be moving faster.

In the Figure, at the instant shown, is the apparent weight of the car's driver greater than, less than, or equal to his true weight?

The apparent weight of the car's driver is less than his true weight.

The gas pedal in a car is sometimes referred to as "the accelerator." Which other controls on the vehicle can be used to produce acceleration?

The brakes

Here's a great everyday use of the physics described in this chapter. If you are trying to get ketchup out of the bottle, the best way to do it is to turn the bottle upside down and give the bottle a sharp upward smack, forcing the bottle rapidly upward. Think about what subsequently happens to the ketchup, which is initially at rest, and use Newton's first law to explain why this technique is so successful.

The inertia of the ketchup will keep it from moving if it isn't too tightly adhered to the sides of the moving bottle.

You are cycling around a circular track at a constant speed. Does the magnitude of your acceleration change? The direction?

The magnitude of the acceleration doesn't change. But the direction does.

An astronaut takes his bathroom scale to the moon and then stands on it. Is the reading of the scale his true weight? Select the correct explanantion.

The reading on the moon will be the moon-weight, or the gravitational force of the moon on the astronaut. This would be about 1/6 of the astronaut's earth-weight or the gravitational force of the earth on the astronaut (while standing on the scales on the earth).

A ball on a string moves in a vertical circle as shown in the Figures. Choose the correct free-body diagram for the case when the ball is at its lowest point.

straight line looking tension > weight