AP Physics Final Questions
An object's average density ρρ is defined as the ratio of its mass to its volume: ρ=M/V. The earth's mass is 5.94×1024kg, and its volume is 1.08×1012km3. What is the earth's average density?
5.50×103kg/m3
A football is kicked at an angle of 35 ∘∘ with a speed of 24 m/s. How far will the ball travel?
55 m
The figure is a motion diagram with the clock reading (in seconds) shown at each position. The positions for t≥ 16 s are offset for clarity, but the motion actually occurs along a single track. Which graph best represents the object's velocity? (Figure 2)
B
Which combination of the vectors shown in (Figure 1) has the largest magnitude?
B + A - C
Velocity-versus-time graphs for three racers are shown in the figure below. Which of the three drag racers had the greatest acceleration at t=0s
Betty
Velocity-versus-time graphs for three racers are shown in the figure. (see image) At t=5.0s, which car has traveled the furthest?
Betty
The following options describe the motion of four cars. Which car has the largest acceleration?
Goes from 0 m/s to 3.8 m/s in 1.0 s
A football is kicked at an angle of 40 ∘ with a speed of 24 m/s. To the nearest second, how long will the ball stay in the air?
3 sec
A 2.5 kg ball is suspended by two light strings as shown in (Figure 1). What is the tension T in the angled string?
32 N
A car coasts at a constant speed over a circular hill.
C
The figure shows the position graph of a car traveling on a straight road as a function of time. At which labeled instant is the speed of the car greatest?
C
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?
Johnathan
Two vectors appear as in the figure. Which combination points directly left?
Q - P
Assume MSaturn= 5.68×1026 kg and RSaturn = 5.82×107 mm . a) What is the value of gg on the surface of Saturn? b) Choose the appropriate explanation how such a low value is possible given Saturn's large mass - 100 times that of Earth.
a) 11.2 m/s^2 b) This low value is possible because the density of Saturn is so low.
a) How fast (in km/h) must a plane fly along the earth's equator so that the sun stands still relative to the passengers? The radius of the Earth is 6400 km. b) Answer the same question in mph. c) In which direction must the plane fly, east to west or west to east?
a) 1700 km/h b) 1040 mph c) east to west
A 3.0 kg puck slides due east on a horizontal frictionless surface at a constant speed of 4.5 m/s . Then a force of magnitude 6.0 N , directed due north, is applied for 1.5 s. a)What is the northward component of the puck's velocity? b)What is the speed of the puck?
a) 3.0 m/s b) 5.4 m/s
A car drives horizontally off a 75-m-high cliff at a speed of 29 m/s . Ignore air resistance. a) How long will it take the car to hit the ground? b) How far from the base of the cliff will the car hit
a) 3.9 s b) 110m
The floor is frictionless. (see image) a) In which direction is the kinetic friction force on block 1 in the figure? b) On block 2?
a) to the right b) to the left
A tennis player hits a ball 2.0 mm above the ground. The ball leaves his racquet with a speed of 20 m/s at an angle 5.0 ∘ above the horizontal. The horizontal distance to the net is 7.0 mm, and the net is 1.0 mm high. a) Does the ball clear the net? b) If so, by how much? If not, by how much does it miss?
a) yes b) 1 m
A Thompson's gazelle can reach a speed of 13 m/s in 3.0 s . A lion can reach a speed of 9.5 m/s in 1.0 s . A trout can reach a speed of 2.8 m/s in 0.12 s . Which animal has the greatest acceleration?
trout
Two football players are pushing a 60 kg blocking sled across the field at a constant speed of 2.0 m/s. The coefficient of kinetic friction between the grass and the sled is 0.30. Once they stop pushing, how far will the sled slide before coming to rest?
0.68 m
Weddell seals make holes in sea ice so that they can swim down to forage on the ocean floor below. Measurements for one seal showed that it dived straight down from such an opening, reaching a depth of 0.30 km in a time of 5.0 min. What was the speed of the diving seal?
1 m/s
A girl stands on a sofa. Identify the number of the action/reaction pairs of forces between the girl and the sofa.
1 pair
Some car manufacturers claim that their vehicles could climb a slope of 44 ∘. For this to be possible, what must be the minimum coefficient of static friction between the vehicle's tires and the road?
1.0
The earth formed 4.57×10+9 years ago. What is this time in seconds?
1.44×10+17s
A person walks briskly at 2.10 m/s.
12.8 min
Suppose you and a friend, each of mass 60 kg , go to the park and get on a 4.5-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 6.5 seconds. What is the magnitude of the (apparent) outward force that you feel?
130 N
A ball thrown at an initial angle of 37.0∘∘ and initial velocity vi = 24.0 m/s reaches a maximum height h, as shown in (Figure 1). With what initial speed must a ball be thrown straight up to reach the same maximum height h?
14.4 m/s
A car can go from 0 to 60 mph in 8.0 s . Assuming that it could maintain the same acceleration at higher speeds, how long would it take the car to go from 0 to 120 mph?
16 s
student walks 1.6 mi west and then 1.6 mi north. Afterward, how far is she from her starting point?
2.3 mi
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?
2/9 g
A football player at practice pushes a 70 kg blocking sled across the field at a constant speed. The coefficient of kinetic friction between the grass and the sled is 0.30. How much force must he apply to the sled?
210 N
The cylindrical space station in (Figure 1), d = 250 mm 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?
22 sec
A truck is traveling at 30 m/s on a slippery road. The driver slams on the brakes and the truck starts to skid. If the coefficient of kinetic friction between the tires and the road is 0.20, how far will the truck skid before stopping?
230 m
A 6.0 kg block has an acceleration of 0.40 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?
24kg
A bird flies 3.6 km due west and then 2.1 km due north. Another bird flies 2.1 km due west and 3.6 km due north. What is the angle between the net displacement vectors for the two birds?
29
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
The figure shows an object's position-versus-time graph. What is the velocity of the object at 6 s?
3.3 m/s
Compute 3.24 m + 0.432 m to the correct number of significant figures.
3.67 m
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 mm at 68 m/s.
30000N
A bird flies 3.8 km due west and then 2.4 km due north. What is the magnitude of the bird's displacement?
4.5 km
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 10 N . What would the tension be if the ball went around in only half a second?
40 N
Blades of grass grow from the bottom, so, as growth occurs, the top of the blade moves upward. During the summer, when your lawn is growing quickly, estimate this speed, in m/s. Make this estimate from your experience noting, for instance, how often you mow the lawn and what length you trim.
4×10−8 m/s
Eric has a mass of 70 kg. He is standing on a scale in an elevator that is accelerating downward at 1.7 m/s2. What is the approximate reading on the scale?
570N
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 mm at a speed of 68 m/s. What is the approximate magnitude of the centripetal acceleration, in units of g?
5g
A car is traveling at vx = 24 m/s . The driver applies the brakes and the car decelerates at ax = -4.0 m/s2 . What is the stopping distance?
72 m
The two block in (Figure 1) are at rest on frictionless surfaces. What must be the mass of the right block in order that the two blocks remain stationary? Suppose that mmm = 16 kg.
9.7 kg
Which of the following motions is described by the motion diagram of the figure?
A car pulling away from a stop sign
Which of the following motions could be described by the motion diagram of the (Figure 1) ?
A cyclist braking to a stop.
Suppose you are an astronaut in deep space, far from any source of gravity. You have two objects that look identical, but one has a large mass and the other a small mass. How can you tell the difference between the two?
Assuming you can exert a reproducible force in throwing both objects, you could throw each and note the acceleration each obtains.
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.(Figure 1) 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 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.
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 then up
As seen from above, a car rounds the curved path shown the figure below at a constant speed. (see image) Which vector best represents the net force acting on the car?
E
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. (Figure 1) 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.
If you are standing still, the upward normal force on you from the floor 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. Explain how this could be done.
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.
Why is it impossible for an astronaut inside an orbiting space station to go from one end to the other by walking normally?
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.
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=Fnet/m. Since both the net force and mass are increased they still cancel, leaving the acceleration the same.
A jet plane is speeding down the runway during takeoff. Air resistance is not negligible. Identify the forces on the jet
Normal force, Thrust, Drag, Weight
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=4r1. Planet 1 orbits with period T1. Planet 2 orbits with period.
T2 = 8T1
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
In (Figure 1), 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.
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.
A beach ball is thrown straight up, and some time later it lands on the sand. Is the magnitude of the net force on the ball greatest when it is going up or when it is on the way down? Or is it the same in both cases? Explain. Air resistance should not be neglected for a large, light object.
The only contact force is the force of air drag on the ball. The only long-range force is the weight of the ball. Drag always points in the direction opposite to the motion. Thus the weight of the ball and the drag force always reinforce each other if the ball is moving straight up. The net force is larger on the way up.
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 explanation.
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).
The tire on this drag racer is severely twisted: The force of the road on the tire is quite large (most likely several times the weight of the car) and is directed forward as shown in (Figure 1) (see image) Is the car speeding up or slowing down? Explain
The way the tire is twisted indicates that the force of the road on the tire is forward. Since this force is likely greater than the backward air resistance force, the net force is also forward; therefore, the car is accelerating in the forward direction.
(Figure 1) 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.
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.
You can't lift yourself off the floor because the net external force on you is still zero.
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
Suppose you are holding a box in front of you and away from your body by squeezing the sides, as shown in (see image on mastering physics) a) Choose the correct free-body diagram showing all of the forces on the box. b) What is the force that is holding the box up, the force that is opposite the weight force?
a) (see image on card) b) static friction force
Scallops eject water from their shells to provide a thrust force. (Figure 1) shows a smoothed graph of actual data for the initial motion of a 25 g scallop speeding up to escape a predator. (see image) a) What is the magnitude of the net force needed to achieve this motion? b) How does this force compare to the 0.25 NN weight of the scallop?
a) 0.025 N b) This force is 1/10 of the weight of the scallop.
(Figure 1) shows an acceleration-versus-force graph for three objects pulled by rubber bands. The mass of object 2 is 0.40 kg. a) What is the mass of object 1? b) What is the mass of object 3? c) Explain your reasoning.
a) 0.16 kg b) 1 kg c) A larger slope implies a smaller mass. We know the mass of object 2, and we can find the other masses relative to m2 by comparing their slopes.
When you blink your eye, the upper lid goes from rest with your eye open to completely covering your eye in a time of 0.024 s. a) Estimate the distance that the top lid of your eye moves during a blink. b) What is the acceleration of your eyelid? Assume it to be constant. c) What is your upper eyelid's final speed as it hits the bottom eyelid?
a) 1 cm b) 35 m/s2 c) 0.84 m/s
A man's higher initial acceleration means that a man can outrun a horse over a very short race. A simple - but plausible - model for a sprint by a man and a horse uses the following assumptions: The man accelerates at 6.0 m/s2 for 1.8 s and then runs at a constant speed. A horse accelerates at a more modest 5.0 m/s2m/s2 but continues accelerating for 4.8 s and then continues at a constant speed. A man and a horse are competing in a 200 mm race. The man is given a 100 mm head start, so he begins 100 mm from the finish line. a) How much time does the man take to complete the race? b) How much time does the horse take? c) Who wins the race?
a) 10.16 s b) 10.73 s c) The man
A stubborn 140 kg pig sits down and refuses to move. To drag the pig to the barn, the exasperated farmer ties a rope around the pig and pulls with his maximum force of 800 N. The coefficients of friction between the pig and the ground are μs=0.80 and μk=0.50 a) Calculate the force which farmer needs to apply to budge the pig. b) Is the farmer able to move the pig?
a) 1100N b) No, the farmer will not be able to budge the pig, because the maximum static friction force is greater than the farmer's maximum pull of 800 N.
Small-plane pilots regularly compete in "message drop" competitions, dropping heavy weights (for which air resistance can be ignored) from their low-flying planes and scoring points for having the weights land close to a target. A plane 65 mm above the ground is flying directly toward a target at 46 m/s. a) At what distance from the target should the pilot drop the weight? b) The pilot looks down at the weight after she drops it. Where is the plane located at the instant the weight hits the ground?
a) 170 m b) directly over the target
A fast pitch softball player does a "windmill" pitch, moving her hand through a vertical circular arc to pitch a ball at 71 mph. The 0.19 kg ball is 53 cm from the pivot point at her shoulder. a) Just before the ball leaves her hand, what is its centripetal acceleration? b) At the lowest point of the circle the ball has reached its maximum speed. What is the magnitude of the force her hand exerts on the ball at this point? c) At the lowest point of the circle the ball has reached its maximum speed. What is the direction of the force her hand exerts on the ball at this point?
a) 1900 m/s2 b) 363 N c) upward
A car is skidding to a stop on a level stretch of road. a) Identify the number of the action/reaction pairs of forces between the car and the road surface. b) Draw a free-body diagram for the car. The car is moving to the left.
a) 2 pairs b) see image
While standing in a low tunnel, you raise your arms and push against the ceiling with a force of 200 N . Your mass is 80 kg. a) What force does the ceiling exert on you? b) What force does the floor exert on you?
a) 200N b) 980N
Your forehead can withstand a force of about 6.0 kN before fracturing, while your cheekbone can only withstand about 1.3 kN. a) If a 140 g baseball strikes your head at 33 m/s and stops in 0.0014 s , what is the magnitude of the ball's deceleration? b) What is the magnitude of the force that stops the baseball? c) What force does the baseball apply to your head? d) Are you in danger of a fracture if the ball hits you in the forehead? e) Are you in danger of a fracture if the ball hits you in the cheek?
a) 24000 m/s2 b) 3300 N c) 3300 N d) no e) yes
A rider on a water slide goes through three different kinds of motion, as illustrated in the figure below. Use the data and details from the figure to answer the following questions. (see image) a) What is the vertical component of the velocity of a rider as he or she hits the water? b) Suppose the designers of the water slide want to adjust the height h above the water so that riders land twice as far away from the bottom of the slide. What would be the necessary height above the water? c) During which section of the motion is the magnitude of the acceleration experienced by a rider the greatest?
a) 3.4 m/s b) 2.4 m c) the second
Heather and Jerry are standing on a bridge 51 mm above a river. Heather throws a rock straight down with a speed of 17 m/s . Jerry, at exactly the same instant of time, throws a rock straight up with the same speed. Ignore air resistance. a) How much time elapses between the first splash and the second splash? b) Which rock has the faster speed as it hits the water?
a) 3.5 s b) both rocks hit at equal speeds
a) If an astronaut can jump straight up to a height of 0.6 m on earth, how high could he jump on the moon? b) On the earth, an astronaut can safely jump to the ground from a height of 1.3 m ; her velocity when reaching the ground is slow enough to not cause injury. From what height could the astronaut safely jump to the ground on the moon? c) On the earth, an astronaut throws a ball straight upward; it stays in the air for a total time of 3.1 s before reaching the ground again. If a ball were to be thrown upward with the same initial speed on the moon, how much time would pass before it hit the ground?
a) 3.6 m b) 7.8 m c) 19 s
In the winter sport of curling, players give a 20 kg stone a push across a sheet of ice. The stone moves approximately 40 mm before coming to rest. The final position of the stone, in principle, only depends on the initial speed at which it is launched and the force of friction between the ice and the stone, but team members can use brooms to sweep the ice in front of the stone to adjust its speed and trajectory a bit; they must do this without touching the stone. Judicious sweeping can lengthen the travel of the stone by 3 m. a) A curler pushes a stone to a speed of 3.0 m/s over a time of 1.6 s . Ignoring the force of friction, how much force must the curler apply to the stone to bring it up to speed? b) The sweepers in a curling competition adjust the trajectory of the stone by c) Suppose that the stone is launched with a speed of 3 m/s and travels 40 m before coming to rest. What is the approximate magnitude of the friction force on the stone? d) Suppose the stone's mass is increased to 40 kg, but it is launched at the same 3 m/s. Which one of the following is true?
a) 38 N b) Decreasing the coefficient of friction between the stone and the ice. c) 2N d) The force of friction would now be greater.
A 4.5 kg dog sits on the floor of an elevator that is accelerating downward at 1.20 m/s2 a) What is the magnitude of the normal force of the elevator floor on the dog? b) What is the magnitude of the force of the dog on the elevator floor?
a) 39 N b) 39 N
a) 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? b) At what angle to the ground should you kick the ball for the maximum "hang time" - that is, the maximum time in the air?
a) 45 deg b) 90 deg
A 1100 kg steel beam is supported by the two ropes shown in (see image) a) Calculate the tension in the rope. b) The rope can support a maximum tension of 6100 N . Is this rope strong enough to do the job? Choose the correct answer and explanation.
a) 6220 N b) No. The tension in the ropes exceeds the maximum value, the ropes will break.
A garden has a circular path of radius 50 m. John starts at the easternmost point on this path, then walks counterclockwise around the path until he is at its southernmost point. a) What is the magnitude of John's displacement? b) What is the direction of John's displacement?
a) 71 m b) SW
The car in (Figure 1) travels at a constant speed along the road shown. (see image) a) At which point(s) its acceleration a = 0 b) Draw the vector showing car's acceleration at the point CC if the acceleration at the point A is drawn.
a) B b) vector Ac should be pointing inside the curve
A ball is fired from a cannon at point 1 and follows the trajectory shown in (Figure 1). Air resistance may be neglected. Five possible vectors are also shown in the figure; the letter E represents the zero vector. a) Which vector best represents the ball's velocity at position 2? b) Which vector best represents the ball's acceleration at position 2? c) Which vector best represents the ball's velocity at position 3? d) Which vector best represents the ball's acceleration at position 3?
a) D b) A c) C d) A
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. a) How does this affect the direction of thrust? b) When might these thrust reversers be useful in practice?
a) If the ejected air is directed forward then thrust force is backward (Newton's 3rd law). b) 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.
A box is being dragged across the floor at a constant speed by a rope pulling horizontally on it. Friction is not negligible. a) Identify all the forces acting on the box. b) Draw a free-body diagram of the box. The box is moving to the right.
a) Weight, Kinetic friction force, Tension, Normal force b) see image
A skydiver has his parachute open and is floating downward through the air at a constant speed. a) Identify all the forces acting on the system skydiver-parachute. b) Draw a free-body diagram of the system skydiver-parachute.
a) air resistance and weight b) see image
Dana has a sports medal suspended by a long ribbon from her rearview mirror. As she accelerates onto the highway, she notices that the medal is hanging at an angle of 11 ∘ from the vertical. a) Does the medal lean toward or away from the windshield? b) What is her acceleration?
a) away b) 1.9 m/s2
If a car stops suddenly, you feel "thrown forward." We'd like to understand what happens to the passengers as a car stops. Imagine yourself sitting on a very slippery bench inside a car. This bench has no friction, no seat back, and there's nothing for you to hold on to. a) Identify all of the forces acting on you as the car travels in a straight line at a perfectly steady speed on level ground. b) Draw your free-body diagram. Suggest that the car is moving to the right. c) Identify all of the forces acting on you as the car slowing down. d) Draw your free-body diagram if the car slowing down. Suggest that the car is moving to the right. e) Describe what happens to you as the car slows down. f) Use Newton's laws to explain why you seem to be "thrown forward" as the car stops. Is there really a force pushing you forward?
a) normal force, weight b) see on mastering physics c) weight, normal force d) see on mastering physics e) You continue to move forward with the initial speed of the car. f) The net force on you has remained zero because the net vertical force is zero and there are no horizontal forces. According to Newton's first law, if the net force on you is zero, then you continue to move in a straight line with a constant velocity. That is what happens to you when the car slows down. You continue to move forward with a constant velocity.
A 77 kg man weighs himself at the north pole and at the equator. a) Which scale reading is higher? b) By how much?
a) north pole b) 2.6 N
A sprinter has just started a race and is speeding up as she runs down the track. The sprinter is running to the right. a) Draw a motion diagram. b) Identify all the forces acting on the sprinter. c) Draw a free-body diagram of the sprinter.
a) see image b) static friction, normal force, weight c) see mastering physics
A 28 kg child goes down a straight slide inclined 38∘∘ above horizontal. The child is acted on by his weight, the normal force from the slide, and kinetic friction. a) Choose the correct free-body diagram of the child. b) How large is the normal force of the slide on the child?
a) see image b) 220 N
A ball on a string moves in a vertical circle as shown in (see mastering physics) a) Choose the correct free-body diagram for the case when the ball is at its lowest point. b) When the ball is at its lowest point, is the tension in the string greater than, less than, or equal to the ball's weight?
a) see image b) The tension in the string is greater than the ball's weight.
You've slammed on the brakes and your car is skidding to a stop while going down a 20∘ hill. a)Select a correct motion diagram for this situation. b) Identify all the forces acting on the car. c) Draw a free-body diagram of the car.
a) see image b) kinetic friction force, normal force, weight c) see image on mastering physics
A spring-loaded gun shoots a plastic ball. The trigger has just been pulled and the ball is starting to move down the barrel. The barrel is horizontal. a) Select a correct motion diagram. b) Identify all the forces acting on the ball. c) Draw a free-body diagram for the ball. Assume the ball is moving to the right.
a) see image b) normal force, kinetic friction force, weight, spring force c) see on mastering physics
A bag of groceries is on the back seat of your car as you stop for a stop light. The bag does not slide. a) Select a correct motion diagram for the bag. b) Identify all the forces c) Draw a free-body diagram for the bag. Suppose that car is moving to the right.
a) see image b) static friction force, normal force, weight c) see on mastering physics
A basketball player is getting ready to jump, pushing off the ground and accelerating upward. a) Select a correct motion diagram. b) Identify all the forces acting on the basketball player. c) Draw a free-body diagram of the basketball player.
a) see image b) weight, normal force c) see mastering physics
An elevator, suspended by a single cable, has just left the tenth floor and is speeding up as it descends toward the ground floor. Neglect the friction. a) Select the correct motion diagram for this situation. b) Identify all the forces acting on the elevator. c)
a) see image b) weight, tension c) see on mastering physics
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.(see image) a) The sum of the three forces acting on the center point of the rope is assumed to be zero because b) When you are pulling on the rope as shown, what is the approximate direction of the tension force on the tree? c) 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? d) 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
a) the point is not accelerating b) East c) East d) Equal to the force of the rope on the car.
A student at the top of a building of height h throws ball A straight upward with speed v0 and throws ball B straight downward with the same initial speed. a) Compare the ball's accelerations, both direction and magnitude, immediately after they leave her hand. Is one acceleration larger than the other? Or are the magnitudes equal? b) Compare the final speeds of the balls as they reach the ground.
a) they are equal b) they are equal
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. a) The direction of the net force on the craft is b) How fast is this spacecraft moving? c) How much time does it take for the spacecraft to complete one orbit? d) 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
a) towards the center of the moon b) 1700 m/s c) 110 min d) away from the surface of the moon
a) For a projectile, which of the following quantities are constant during the flight: x, y, vx, vy, v, ax, ay? b) Which of the quantities are zero throughout the flight?
a) vx, vy, ay b) ax
Your car is skidding to a stop from a high speed. a) Identify all forces acting on the object. b) Draw a free-body diagram of the car. Suppose that the car is moving to the right.
a) weight, normal force, air resistance, kinetic friction force b) see image
You are driving on the highway, and you come to a steep downhill section. As you roll down the hill, you take your foot off the gas pedal. You can ignore friction, but you can't ignore air resistance. a) Identify all the forces acting on the car. b) Draw a free-body diagram of the car.
a) weight, normal force, drag b) see image
An ascending elevator, hanging from a cable, is coming to a stop. a) Identify all forces acting on the elevator from the list below. b) Draw a free-body diagram of the object.
a) weight, tension b) see image
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?
all of the above (brakes, steering wheel, and gear shift)
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
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
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
A falcon is hovering above the ground, then suddenly pulls in its wings and begins to fall toward the ground. Air resistance is not negligible. Identify the forces on the falcon.
drag and weight
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
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
In uniform circular motion, which of the following quantities are constant?
magnitude of the net force, speed
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 wood block in the figure below is at rest on a wood ramp. (see image) In which direction is the static friction force on block 1?
not enough info to tell
You throw a rock upward. The rock is moving upward, but it is slowing down. If we define the ground as the origin, the position of the rock is _____ and the velocity of the rock is _____.
positive, positive
A 1.0 kg wood block is pressed against a vertical wood wall by a 12 N force as shown in the figure. (Use μs=0.5 for wood on wood.)(Figure 1)
stay at rest
A baseball player is sliding into second base. Identify the forces on the baseball player.
weight, normal force, kinetic friction
A skier is sliding down a 15∘ slope. Friction is not negligible. Identify the forces on the skier.
weight, normal force, kinetic friction
A mountain climber is hanging from a vertical rope, far above the ground and far from the rock face. The rope is vertical. Identify the forces on the mountain climber.
weight, tension
You look up from your textbook and observe a spider, motionless above you, suspended from a strand of spider silk attached to the ceiling. You distract yourself by identifying the forces acting on the spider. What are they?
weight, tension
We set the origin of a coordinate system so that the position of a train is x = 0 m at tt = 0 s. (Figure 1) shows the train's velocity graph. (see image) a) Choose the correct position graph for the train. b) Choose the correct acceleration graph for the train. c) Find the acceleration of the train at t= 3.0 s.
a) (see mastering for answer) b) (see mastering for answer) c) 1 m/s^2
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 (see image) a) How long does it take for the ball to hit the wall? b) At what height h does the ball hit the wall?
a) 4.4 s b) 160 m
A 200 kg weather rocket is loaded with 100 kg of fuel and fired straight up. It accelerates upward at 30.0 m/s2 for 30.0 s, then runs out of fuel. Ignore any air resistance effects. a) What is the rocket's maximum altitude? b) How long is the rocket in the air? c) Choose the correct velocity-versus-time graph for the rocket from liftoff until it hits the ground.
a) 54.8 km b) 227 s c) (see image)
The images of trees in the figure come from a catalog advertising fast-growing trees. If we mark the position of the top of the tree in the successive years, as shown in the graph in the figure, we obtain a motion diagram much like ones we have seen for other kinds of motion. The motion isn't steady, of course. In some months the tree grows rapidly; in other months, quite slowly. We can see, though, that the average speed of growth is fairly constant for the first few years. a) What is the tree's speed of growth, in feet per year, from t=1yr to t=3yr? b) What is the tree's speed in m/s? c) At the end of year 3, a rope is tied to the very top of the tree to steady it. This rope is staked into the ground 15 feet away from the tree. What angle does the rope make with the ground?
a) 9ft/yr b) 9×10−8m/s c) 63
a) Choose an example of a vertical motion with a positive velocity and a negative acceleration. b) Choose an example of a vertical motion with a negative velocity and a negative acceleration.
a) A ball thrown upward, before it starts to fall back down. b) A ball dropped from a height during its downward motion.
(Figure 1) shows the position graph for an object moving along the horizontal axis. (see image) Write a realistic motion short story for an object that would have this position graph.
a) A fencer is initially still. To avoid his opponent's lunge, the fencer jump(s) backwards very quickly. He remains still for a few seconds. The fencer then begins to advance(s) slowly on his opponent. b) (choice d on mastering)
The figure shows a position-versus-time graph. (see image) a)At which lettered point or points is the object moving the fastest? b) At which lettered point or points is the object moving to the left (in the negative x-direction)? c) At which lettered point or points is the object speeding up? d) At which lettered point or points is the object slowing down? e) At which lettered point or points is the object turning around?
a) D b) C,D,E c) C d) A & E e) B
Suppose two vectors have unequal magnitudes. Can their sum be 0?
no
A rectangle has length 3.24 mm and height 0.432 mm . To the correct number of significant figures, what is its area?
1.40 m^2
Estimate the average speed, in m/s, with which the hair on your head grows. Make this estimate from your own experience noting, for instance, how often you cut your hair and how much you trim.
10^-8 m/s
A car can go from 0 to 60 mph in 14 s . A second car is capable of twice the acceleration of the first car. Assuming that it could maintain the same acceleration at higher speeds, how much time will this second car take to go from 0 to 120 mph?
14 s
Riders on a Ferris wheel move in a circle with a speed of 4.50 m/s. As they go around, they experience a centripetal acceleration of 2.40 m/s2. What is the diameter of this particular Ferris wheel?
16.9 m
Motor neurons in mammals transmit signals from the brain to skeletal muscles at approximately 25 m/s Estimate how much time in ms (10−3s) it will take for a signal to get from your brain to your hand.
40 ms
Suppose a plane accelerates from rest for 30 s, achieving a takeoff speed of 80 m/s after traveling a distance of 1200 mm down the runway. A smaller plane with the same acceleration has a takeoff speed of 56 m/s . Starting from rest, after what distance will this smaller plane reach its takeoff speed?
588 m
You are standing on a straight stretch of road and watching the motion of a bicycle; you choose your position as the origin. At one instant, the position of the bicycle is negative and its velocity is positive. Is the bicycle getting closer to you or farther away? Explain.
If the position of the bicycle is negative it is to your left. The bicycle's velocity is positive, or to the right, so the bicycle is getting closer to you.
A car travels along a straight east-west road. A coordinate system is established on the road, with x increasing to the east. The car ends up 16 mi west of the origin, which is defined as the intersection with Mulberry Road. If the car's displacement was -27 mi , what side of Mulberry Road did the car start on? How far from the intersection was the car at the start?
The car started 11 mi east of Mulberry Road.
The bacterium Escherichia coli (or E. coli) is a single-celled organism that lives in the gut of healthy humans and animals. Its body shape can be modeled as a 2-μmμm-long cylinder with a 1 μmμm diameter, and it has a mass of 1×10−12 g. Its chromosome consists of a single double-stranded chain of DNA 700 times longer than its body length. The bacterium moves at a constant speed of 20 μm/s though not always in the same direction. Answer the following questions about E. coli using SI units (unless specifically requested otherwise) and correct significant figures. a) What is its length? b) What is its diameter? c) What is its mass? d) What is the length of its DNA, in millimeters? e) If the organism were to move along a straight path, how many meters would it travel in one day?
a) 2×10−6m b) 1×10−6m c) 1×10−15kg d) 1mm e) 2m
In 1780, in what is now referred to as "Brady's Leap," Captain Sam Brady of the U.S. Continental Army escaped certain death from his enemies by running over the edge of the cliff above Ohio's Cuyahoga River in (Figure 1), which is confined at that spot to a gorge. He landed safely on the far side of the river. It was reported that he leapt 22 ft (≈6.7 mm) across while falling 20 ft (≈6.1 mm). a) What is the minimum speed with which he'd need to run off the edge of the cliff to make it safely to the far side of the river? b) The world-record time for the 100 mm dash is approximately 10 s. Given this, is it reasonable to expect Brady to be able to run fast enough to achieve Brady's leap?
a) 5.998 m/s b) Yes, the obtained speed is less than the world-record.
A rider on a water slide goes through three different kinds of motion, as illustrated in the figure. Use the data and details from the figure to answer the following questions. (see image) a) At the end of the first section of the motion, riders are moving at what approximate speed? b) Suppose the acceleration during the second section of the motion is too large to be comfortable for riders. What change could be made to decrease the acceleration during this section? c) What is the vertical component of the velocity of a rider as he or she hits the water? d) Suppose the designers of the water slide want to adjust the height above the water so that riders land twice as far away from the bottom of the slide. What would be the necessary height above the water? e)During which section of the motion is the magnitude of the acceleration experienced by a rider the greatest?
a) 9 m/s b)Increase the radius of the circular segment. c) 3.4 m/s d) 2.4m e) second
The bacterium Escherichia coli (or E. coli), is a single-celled organism that lives in the gut of healthy humans and animals. When grown in a uniform medium rich in salts and amino acids, it swims along zig-zag paths at a constant speed. (Figure 1) shows the positions of an E. coli as it moves from point A to point J. Each segment of the motion can be identified by two letters, such as segment BC. a) During which segments, if any, does the bacterium have the same displacement? b) During which segments, if any, does the bacterium have the same speed? c) During which segments, if any, does the bacterium have the same velocity?
a) AB and CD b) all paths c) AB and CD
(Figure 1) is the velocity-versus-time graph for an object moving along the x-axis. a) During which segment(s) is the velocity constant? b) During which segment(s) is the object speeding up? c) During which segment(s) is the object slowing down? d) During which segment(s) is the object standing still? e) During which segment(s) is the object moving to the right (in the positive x-direction)?
a) ADF b) C c) BE d) F e) AB
A ball is thrown straight up into the air. At each of the following instants, is the ball's acceleration Ay equal to g, −g, 0, <g, or >g? a) Just after leaving your hand? b) At the very top (maximum height)? c) Just before hitting the ground?
a) Ay = -g b) Ay = -g c) Ay = -g
A car travels at constant speed along the curved path shown in (Figure 1). Five possible vectors are also shown in the figure; the letter E represents the zero vector. (see image) a) Which vector best represents the car's velocity at position 1? b) Which vector best represents the car's acceleration at point 1? c) Which vector best represents the car's velocity at position 2? d) Which vector best represents the car's acceleration at point 2? e) Which vector best represents the car's velocity at position 3? f) Which vector best represents the car's acceleration at point 3?
a) B b) E c) C d) D e) B f) A
Two cars travel on the parallel lanes of a two-lane road. The cars' motions are represented by the position versus time graph shown in the figure. Answer the questions using the times from the graph indicated by letters. (see image) a) At which of the times do the two cars pass each other? b) Are the two cars traveling in the same direction when they pass each other? c) At which of the lettered times, if any, does car #1 momentarily stop? d) At which of the lettered times, if any, does car #2 momentarily stop? e) At which of the lettered times are the cars moving with nearly identical velocity?
a) D b) no c) none d) c e) a
A Porsche challenges a Honda to a 400 mm race. Because the Porsche's acceleration of 3.4 m/s2 is larger than the Honda's 3.0 m/s2, the Honda gets a 110 mm head start - it is only 290 mm from the finish line. Assume, somewhat unrealistically, that both cars can maintain these accelerations the entire distance. a) Who wins the race? b) By how much time does the winner win?
a) Honda b) 1.4 s
a) Determine the sign (positive or negative) of the position and the velocity for the motion diagram in (Figure 1) b) Determine the sign (positive or negative) of the position and the velocity for the motion diagram in (Figure 2) c) Determine the sign (positive or negative) of the position and the velocity for the motion diagram in (Figure 3)
a) Negative position, positive velocity b) Negative position, negative velocity c) Positive position, negative velocity
An object moves along the x axis during four separate trials. Graphs of position versus time for each trial (with the same scales on each axis) are shown in the figure. a) During which trial or trials is the object's velocity not constant? b) During which trial or trials is the magnitude of the average velocity the largest?
a) Trial B b) B + D
An airplane has been directed to fly in a clockwise circle, as seen from above, at constant speed until another plane has landed. a) When the plane is going north, is it accelerating? b) When the plane is going north, in what direction does the acceleration vector point?
a) 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. b) east
In physics, every physical quantity is measured with respect to a unit. Time is measured in seconds, length is measured in meters, and mass is measured in kilograms. Knowing the units of physical quantities will help you solve problems in physics. a) For this equation to have consistent units, the units of G must be which of the following? b) the units of E must be which of the following?
a) m^3 / kg*s^2 b) kg*m^2 / s^2
Shannon decides to check the accuracy of her speedometer. She adjusts her speed to read exactly 70 mph on her speedometer and holds this steady, measuring the time between successive mile markers separated by exactly 1.00 mile. a) If she measures a time of 47 ss , is her speedometer accurate? b) If not, is the speed it shows too high or too low?
a) no b) too low
For each motion diagram shown in the figure, determine the sign (positive or negative) of the acceleration.
a) positive b) negative c) negative
The minimum stopping distance for a car traveling at a speed of 30 m/s is 60 mm, including the distance traveled during the driver's reaction time of 0.50 s . a) Select the correct position-versus-time graph for the motion of the car. Assume the car is at xi = 0 mm when the driver first sees the emergency situation ahead that calls for a rapid halt. b) What is the minimum stopping distance for the same car traveling at a speed of 43 m/s?
a) see image b) 114 m
Does a real automobile have constant acceleration? Measured data for a Porsche 944 Turbo at maximum acceleration are as follows: (table on mastering physics) a) Convert the velocities to m/s, then choose the correct graph of velocity versus time. b) Based on your graph, is the acceleration constant? c) Use your graph to estimate the car's acceleration at 2.0 s. Give your answer in SI units. d) Use your graph to estimate the car's acceleration at 8.0 ss. Give your answer in SI units.
a) see image b) No, it decreases with increasing time. c) 5.1 m/s^2 d) 2 m/s^2
A sports car is advertised as capable of "reaching 60 mph in 5 seconds flat, cornering at 0.85g, and stopping from 70 mph in only 168 feet." a) In which of those three situations is the magnitude of the car's acceleration the largest? b) In which of those three situations is the magnitude of the car's acceleration the smallest?
a) stopping at 70 mph in only 168 ft b) reaching 60 mph in 5 sec flat
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. a) In each of the following segments of the motion, are the cars accelerating, or is their acceleration zero? b) Which way does their acceleration vector point as the cars roll up the ramp? c) Which way does their acceleration vector point at the highest point on the ramp? d) Which way does their acceleration vector point as the cars roll back down the ramp?
a) the cars are accelerating as the cars roll up the ramp, as the cars roll down the ramp, and at the highest point on the ramp b) downward along the ramp c) downward along the ramp d) downward along the ramp
(Figure 1) shows the motion diagram for a rider on a Ferris wheel that was turning at a constant speed. The inset to the figure shows how to find the acceleration vector at the rightmost point. a) Use a similar analysis to find the rider's acceleration vector at the leftmost position of the motion diagram in (Figure 2 on mastering) b) Find the rider's acceleration vector at the highest position of the motion diagram in (Figure 3 on mastering) c) Find the rider's acceleration vector at the lowest position of the motion diagram in (Figure 3 mastering)
a) v = v7 - v6 b) v = v4 - v3 c) v = v9 - v8
The figure below shows an object's position-versus-time graph. The letters A to E correspond to various segments of the motion in which the graph has constant slope. a) In which segment(s) is the object at rest? b) In which segment(s) is the object moving to the right (in the positive x direction)? c) Is the speed of the object during segment C greater than, equal to, or less than its speed during segment E?
a)B + D b) A c) greater
The figure shows the position graph of a car traveling on a straight road. (see image) The velocity at instant 1 is _________ and the velocity at instant 2 is _________.
negative, negative
