AP Physics Semester 1 Chapter 3

Three blocks are sliding together to the right along a surface of negligible friction when a force with magnitude Fext is exerted to the left on the rightmost block, as shown in the figure. The masses of the blocks are indicated in the figure. If the force is exerted for a time Δt, what is the change in velocity of the center of mass of the three-block system?

(Fext/6m)Δt

A 50.0 N box is at rest on a horizontal surface. The coefficient of static friction between the box and the surface is 0.50, and the coefficient of kinetic friction is 0.30. A horizontal 20.0 N force is then exerted on the box. The magnitude of the acceleration of the box is most nearly

0

The cart of mass 10 kg shown above moves without frictional loss on a level table. A 10 N force pulls on the cart horizontally to the right. At the same time, a 30 N force at an angle of 60° above the horizontal pulls on the cart to the left. What is the magnitude of the horizontal acceleration of the cart?

0.5

Three objects can only move along a straight, level path. The graphs below show the position d of each of the objects plotted as a function of time t. The sum of the forces on the object is zero in which of the cases?

1 and 2 only

Three forces act on an object. If the object is in translational equilibrium, which of the following must be true? I. The vector sum of the three forces must equal zero II. The magnitudes of the three forces must be equal III. All three forces must be parallel.

1 only

A 2 kg block, starting from rest, slides 20 m down a frictionless inclined plane from X to Y, dropping a vertical distance of 10 m as shown above. The magnitude of the net force on the block while it is sliding is most nearly

10

To analyze the characteristics and performance of the brakes on a 1500 kg car, researchers collected the data shown in the table above. It shows the car's speed when the brakes are first applied and the corresponding braking distance required to stop the car. The magnitude of the average braking force on the car is most nearly

12,000N

The free body diagram shown above is for a 5 kg box on a rough surface being pulled to the right at a constant speed by a string that is at an angle of 30° above the horizontal. The coefficient of kinetic friction between the box and the surface is 0.30. The tension in this string is most nearly

14.47 N

The two blocks eventually stop and reverse direction. Which of the following graphs best predicts the acceleration of block A as it moves up and down the rough, inclined surface? Assume that the positive direction points down the slope.

2 lines separate above x axis

The inclined plane in the figure above has two sections of equal length and different roughness. The dashed line shows where section 1 ends and section 2 begins. A block of mass M is placed at different locations on the incline. The coefficients of kinetic and static friction between the block and each section are shown in the table below. If the block is sliding up section 2, what is the magnitude of the force of friction that is exerted on the block by the incline?

2 μk Mg cos θ

The figure above shows the forces exerted on a block that is sliding on a horizontal surface: the gravitational force of 40 N, the 40 N normal force exerted by the surface, and a frictional force exerted to the left. The coefficient of friction between the block and the surface is 0.20. The acceleration of the block is most nearly

2.0 m/s2 to the left

Block A is placed on a rough surface inclined at an angle θ above the horizontal. A taut string connects block A over a pulley to block B, which hangs from the string, as shown below. The masses of blocks A and B are MA and MB, respectively. At time t=0, block A is sliding up the slope as block B falls, and the blocks are both slowing down. Assume that the mass and friction of the pulley are negligible.

20N

A box is given a sudden push up a ramp. Friction between the box and the ramp is not negligible. Which of the following diagrams best represents the directions of the actual forces acting on the box as it moves upward after the push?

3 arrows one to the left one up one down

The system shown above is released from rest. If friction is negligible, the acceleration of the 4.0 kg block sliding on the table shown above is most nearly

3.3

An Atwood's machine is set up by suspending two blocks connected by a string of negligible mass over a pulley, as shown above. The blocks are initially held at rest and then released at time t0=0 s. The speed of the 3 kg block at time t1=2.0 s is most nearly

4

The following figures each show vectors representing the forces exerted on an object that is initially at rest. In which case will the object remain at rest?

5 arrows one north east south west and one nw

A rope of negligible mass supports a block that weighs 30 N, as shown above. The breaking strength of the rope is 50 N. The largest acceleration that can be given to the block by pulling up on it with the rope without breaking the rope is most nearly

6.7

Block A of mass 4m is attached by a light string to block B of mass 2m. The string passes over a pulley with negligible friction and of negligible mass. Block A is held a distance h above the ground, as shown. The blocks are released from rest, and block A reaches the ground two seconds later. The value of h is most nearly

6.7m

The table shows experimental data of the magnitude of four forces exerted on a 2kg object as it slides across a horizontal surface. Which of the following could represent the magnitude of the net force that is exerted on the object? Select two answers.

6N and 10N

A 5kg object is released from rest near the surface of a planet such that its gravitational field is considered to be constant. The mass of the planet is unknown. After 2s, the object has fallen 30m. Air resistance is considered to be negligible. What is the gravitational force exerted on the 5kg object near the planet's surface?

75N

A block of mass 2 kg slides along a horizontal tabletop. A horizontal applied force of 12 N and a vertical applied force of 15 N act on the block, as shown above. If the coefficient of kinetic friction between the block and the table is 0.2, the frictional force exerted on the block is most nearly

7N

Given the net forces on and the masses of the blocks shown above, which two blocks have the same acceleration? Select two answers.

Block A and D

Two blocks of mass 2 kg and 3 kg are connected by a light string that passes over a pulley, as shown above. The pulley has negligible mass and friction. The two-block system is released from rest. Which of the following correctly describes the velocity of the two-block system's center of mass?

Direction of Velocity=Downward Magnitude of Velocity=Increasing

An object of mass M is dropped near the surface of Earth such that the gravitational field provides a constant downward force on the object. Which of the following describes what happens to the center of mass of the object-Earth system as the object falls downward toward Earth?

Does not move

A 3kg object experiences a rightward horizontal acceleration of 6m/s2 as it slides to the right across a rough, horizontal surface. The table above contains the label and magnitude of four forces exerted to the right or left on the object that represent measurements from an experiment as the object accelerates. Which pair of opposing forces in which directions could be responsible for the acceleration of the object?

F3 to the right and F2 to the left

The graph above shows velocity v as a function of time t for a 0.50 kg object traveling along a straight line. The graph has three segments labeled 1, 2, and 3. A rope exerts a constant force of magnitude FT on the object along its direction of motion the whole time. During segment 2 only, a frictional force of magnitude Ff is also exerted on the object. Which of the following expressions correctly relates the magnitudes Ff and FT?

FT < Ff < 2FT

Three boxes are pulled to the left by strings with negligible mass on a horizontal surface, as shown above. The masses of the boxes are m1, m2, and m3, where m3>m2>m1. Friction between the boxes and the surface is negligible. The figure below shows force diagrams for each box. Which of the following is a correct ranking of the normal forces Fn1, Fn2, and Fn3 exerted on the boxes?

Fn3>Fn2>Fn1

Two blocks are connected by a rope, as shown above. The masses of the blocks are 5 kg for the upper block and 10 kg for the lower block. An upward applied force of magnitude F acts on the upper block. If the net acceleration is downward but has a magnitude less than g, then which has the larger magnitude, the force F or the tension in the rope?

Force F

A 1kg block is placed near the top of an inclined plane that is at an angle of 30 degrees with respect to the ground, as shown above. By correctly determining the effect of gravity, a student predicts that the acceleration of the block will be 5m/s2. After allowing the block to slide down the inclined plane, the student finds that the acceleration is actually 4m/s2. What type of force did the student most likely not account for when predicting the acceleration of the block, and what is the magnitude of that force?

Force of friction of approximately 1N

A person kicks a ball into the air with a force F0. The figure shows the position of the ball at various times. What is the net force on the ball and its acceleration at the highest point shown?

Force=mg+F0 Acceleration=g

A hockey player uses a hockey stick to hit a puck such that the stick provides an applied force on the puck. The puck travels for distance of 0.85m while experiencing the force from the stick. The puck leaves the stick with a speed of 8.0m/s and travels at constant speed in a straight line along the horizontal ice for a distance of 12m. The frictional force between the puck and the ice surface is negligible. How does the magnitude of the force exerted by the stick on the puck Fpuck,stick compare to the magnitude of the force exerted by the puck on the stick Fstick,puck at the time interval in which the stick is in contact with the puck?

Fpuck,stick=Fstick,puck

A motorized cart is attached to a string that passes over a pulley. The other end of the string is attached to a hanging block. In the figure shown above, the cart is accelerating to the right. Which of the following best represents the forces acting on the cart at the instant shown?

Gravity up and down, applied force more than tension

A box of mass m hangs from massless strings, as shown in the figure above. The angle between strings 1 and 2 is 90o, and the angles that the strings make with the ceiling are Ѳ1 and Ѳ2, respectively. If T1 is the tension in string 1, which of the following are the magnitudes of the horizontal and vertical components of the tension in string 2 ?

Horizontal Component: T1cosθ1 Vertical Component: mg−T1sinθ1

The stacks of boxes shown in the figure above are inside an elevator that is moving upward. The masses of the boxes are given in terms of the mass M of the lightest box. Assume the elevator has upward acceleration a, and consider the stack that has two boxes of mass M. What is the magnitude of the force exerted on the top box by the bottom box?

M (a + g)

A toy car has a battery-powered fan attached to it such that the fan creates a constant force that is exerted on the car so that it is propelled in the opposite direction in which the fan blows air. The car has a carriage that allows a student to attach objects of different masses, as shown above. The fan has only one speed setting. All frictional forces are considered to be negligible. Which of the following procedures could be used to determine how the mass of the fan-car-object system affects the acceleration of the system?

Measure the mass of the system using a balance, activate the fan, measure the distance traveled by the system at a known time by using a stopwatch, and repeat the experiment for several trials with different objects added to the carriage.

A block of mass M is attached to a modified Atwood machine and is accelerated upward at 3a by a constant force F0. What is the weight of the bloc

Mg

A block is placed on an inclined plane and remains stationary, as shown in the figure above. A student claims, "The block remains stationary because as gravity tries to pull the block down the ramp, the block exerts an equal and opposite force on itself up the ramp." Is the student's claim correct? Justify your answer.

No. Newton's third law states the block cannot exert a force on itself.

An astronaut in deep space is at rest relative to a nearby space station. The astronaut needs to return to the space station. A student makes the following claim: "The astronaut should position her feet pointing away from the space station. Then, she should repeatedly move her feet in the opposite direction to each other. This action will propel the astronaut toward the space station." Is the student's claim correct? Justify your selection.

No. The astronaut's feet are not exerting a force on another object, so there is no external force to accelerate the astronaut toward the space station.

At time t=0s, object X of mass M travels at a constant speed of 2 m/s to the right toward object Y of mass 2M that is a distance of 8m away from object X while at rest, as shown above. Both objects are on a horizontal surface, where the frictional forces may be considered negligible. Which of the following pairs of force diagrams represents the forces exerted on object X and object Y at t=4 s?

Object X: smaller version of y, towards the left, Object Y: bigger version of x, towards the right

Block A hangs from a light string that passes over a light pulley and is attached to block B, which is on a level horizontal frictionless table, as shown above. Students are to determine the mass of block B from the motion of the two-block system after it is released from rest. They plan to measure the time block A takes to reach the floor. The students must also take which of the following measurements to determine the mass of block B?

Only the mass of block A and the distance block A falls to reach the floor

Identical spheres are dropped from a height of 100m above the surfaces of both Planet X and Planet Y. The position of the spheres as a function of time is recorded as the spheres fall. These data are shown in the graphs above. Which planet exerts a greater gravitational force on the sphere, and what evidence supports this conclusion?

Planet Y, because the magnitude of the slope of the curve increases at a faster rate.

By collecting the appropriate data, the students can determine the relationship between the acceleration of the cart and the net force exerted on the cart. Which of the following graphs should the students produce to show the correct relationship?

Positive linear line starting at (0,0)

Consider the dart-potato system. Which of the following graphs best represents the speed v of the center-of-mass of the dart-potato system, as a function of time t, before, during, and after the collision?

Positive linear slope

Two ice skaters, Skater X and Skater Y, are at rest on a horizontal surface made of ice. The friction between the ice and the skaters is negligible. Skater X, who has a smaller mass than Skater Y, pushes Skater Ysuch that Skater Y travels with a speed of 2vo to the right. Which of the following indicates the direction of the velocity of Skater X and the direction of the velocity of the center of mass of the two-skater system after the push?

Skater X= To the left Center of Mass=Zero

The system shown above consists of two identical blocks that are suspended using four cords, each of a different length. Which of the following claims are true about the magnitudes of the tensions in the cords? Select two answers.

T1cos30°=T2cos60°, T3>T4

Three blocks with masses m1, m2, and m3 are attached by strings, as shown in the figure above. The coefficient of friction between each of the blocks and the horizontal surface is μ. The tension in the left and right strings is T2 and T1, respectively. If the acceleration of the blocks is a, which of the following expressions is equal to T2 ?

T1−m2a−μm2g

Three boxes are pulled to the left by strings with negligible mass on a horizontal surface, as shown above. The masses of the boxes are m1, m2, and m3, where m3>m2>m1. Friction between the boxes and the surface is negligible. The figure below shows force diagrams for each box. Given that m3>m2>m1, how do the force F and string tensions TA and TB compare?

TB<TA<F

Three identical blocks, X, Y, and Z, hang from identical strings, as shown in the figure. Which of the following free-body diagrams could represent the forces exerted on block Y?

Tension Up, Tension Down, Gravity down

An object is at rest on the ground. The object experiences a downward gravitational force from Earth. Which of the following predictions is correct about why the object does not accelerate downward? Select two answers. Justify your selections.

The bonded molecules of the object are repelled upward by the bonded molecules of the ground with the same magnitude as the gravitational force downward on the object., The normal force is exerted upward on the object from the ground with the same magnitude as the gravitational force downward on the object.

A 1500kg car traveling along a road is hit by a 0.1kgrock that creates a small crack in the car's windshield. Which of the following describes the interaction between the windshield and the rock?

The car exerts a force on the rock, and the rock exerts a force on the car. The two forces are equal in magnitude.

A small cart is rolling freely on an inclined ramp with a constant acceleration of 0.50 m/s2 in the -x direction. At time t = 0, the cart has a velocity of 2.0 m/s in the +x-direction. If the cart never leaves the ramp, which of the following statements correctly describes the motion of the cart at a time t > 5

The cart is traveling in the -x-direction and is speeding up.

Two students, Student X and Student Y, stand on a long skateboard that is at rest on a flat, horizontal surface, as shown. In order to get the student-student-skateboard system to accelerate, Student X claims that Student Y should apply a force on Student X while both students stand on the skateboard. Which of the following statements is true regarding the claim made by Student X?

The claim is incorrect because both students are internal to the student-student-skateboard system, and internal forces within a system cannot cause the system to accelerate.

Two objects, X and Y, move toward one another and eventually collide. Object X has a mass of 2M and is moving at a speed of 2v0to the right before the collision. Object Y has a mass of M and is moving at a speed of v0 to the left before the collision. Which of the following describes the magnitude of the forces F the objects exert on each other when they collide?

The force exerted by X on Y is F to the right, and the force exerted by Y on X is F to the left.

A student pulls a block over a rough surface with a constant force FP that is at an angle θ above the horizontal, as shown above. If FP remains constant but the angle θ is increased, which of the following is true at some later time?

The force of friction between the block and surface will decrease.

An object travels down a ramp at a constant acceleration. The object experiences a force of friction and a gravitational force. Which of the following could be true about the motion of the object?

The force of friction between the surface and the object is less than the component of the gravitational force that is parallel to the ramp.

Students connect a spring scale to a block on a rough horizontal surface. The students use the spring scale to measure the magnitude of the horizontal force needed to pull the block at a constant speed. Which of the following statements explains why two forces exerted between objects are equal in magnitude?

The frictional forces that the block and the surface exert on each other, because objects always exert forces of equal magnitude on each other.

A satellite orbits Earth. The only force on the satellite is the gravitational force exerted by Earth. How does the satellite's acceleration compare to the gravitational field at the location of the satellite? Select two answers.

The gravitational field and the acceleration point in the same direction., The magnitudes of the acceleration and the gravitational field strength are equal.

A ball is moved from Earth to a planet that has a gravitational acceleration that is double that of Earth. How does the gravitational force on the ball when it is on the new planet compare to the gravitational force on the ball when it is on Earth?

The gravitational force on the ball when it is on the new planet is double the force on the ball when it is on Earth.

A ladybug is crawling up a wall at constant speed, as shown above. Which of the following are correct justifications for how forces help the ladybug move up the wall? Select two answers.

The ladybug exerts a downward force on the wall to move itself up the wall., The ladybug exerts a downward force on the wall to move itself up the wall.

A spring-loaded launcher has a mass of 0.60 kg and is placed on a platform 1.2m above the ground. The force of friction is negligible between the platform and the launcher. The launcher fires a 0.30kg ball that lands a distance D to the right of the platform, as shown in the diagram above. Which of the following explanations is true?

The launcher will fall off the platform and land D2 to the left of the platform because the launcher is twice the mass of the ball.

A ladder at rest is leaning against a wall at an angle. Which of the following forces must have the same magnitude as the frictional force exerted on the ladder by the floor?

The normal force exerted on the ladder by the wall

A falling skydiver opens his parachute. A short time later, the weight of the skydiver-parachute system and the drag force exerted on the system are equal in magnitude. Which of the following statements predicts the motion of the skydiver at this time?

The skydiver is moving downward with constant speed.

A student sets up an experiment to determine the inertial mass of a cart. The student has access to the following measurement equipment: a spring scale, a meterstick, and a stopwatch. The student uses the spring scale to pull the cart starting from rest along a horizontal surface such that the reading on the spring scale is always constant. All frictional forces are negligible. In addition to the spring-scale reading, which two of the following quantities could the student measure with the available equipment and then use to determine the inertial mass of the cart? Select two answers.

The total distance traveled by the cart after it has been in motion, The time during which the cart is in motion

A cart with an unknown mass is at rest on one side of a track. A student must find the mass of the cart by using Newton's second law. The student attaches a force probe to the cart and pulls it while keeping the force constant. A motion detector rests on the opposite end of the track to record the acceleration of the cart as it is pulled. The student uses the measured force and acceleration values and determines that the cart's mass is 0.4kg

The track was not level and was tilted slightly downward.

Three boxes are pulled to the left by strings with negligible mass on a horizontal surface, as shown above. The masses of the boxes are m1, m2, and m3, where m3>m2>m1. Friction between the boxes and the surface is negligible. The figure below shows force diagrams for each box. Students attach a force probe in the middle of string A to measure TA and then use a different force probe to provide the applied force F to the box of mass m1. With the box of mass m3 held in place by one student, a second student pulls to the left on the force probe that provides the applied force F. As the second student pulls with a steady force, and with the boxes remaining at rest, the following pairs of readings from the two force probes are recorded at different times. Based on the measurements above, how do the magnitudes of the two force quantities compare?

The two quantities agree within experimental uncertainty but do not exactly agree numerically.

A hockey player uses a hockey stick to hit a puck such that the stick provides an applied force on the puck. The puck travels for distance of 0.85m while experiencing the force from the stick. The puck leaves the stick with a speed of 8.0m/s and travels at constant speed in a straight line along the horizontal ice for a distance of 12m. The frictional force between the puck and the ice surface is negligible. Which of the following statements best describes the force or forces exerted on the puck after it is hit by the stick and slides on the ice?

There is no frictional force exerted on the puck, and the gravitational force and normal force are exerted on the puck and are equal in magnitude.

A student uses an electronic force sensor to study how much force the student's finger can apply to a specific location. The student uses one finger to apply a force on the sensor, and data collected from two trials are shown in the table. During which trial, if any, does

Trial 2, because the student's finger applied the largest force to the sensor.

Two astronauts of identical mass are connected by a taut cable of negligible mass, as shown in the figure above, and are initially at rest with respect to a nearby space station. Astronaut Y pulls on the cable toward herself with considerable force. Which of the following describes the direction of the velocity of the center of mass of the two astronauts after Astronaut Y pulls on the cable?

Two astronauts of identical mass are connected by a taut cable of negligible mass, as shown in the figure above, and are initially at rest with respect to a nearby space station. Astronaut Y pulls on the cable toward herself with considerable force. Which of the following describes the direction of the velocity of the center of mass of the two astronauts after Astronaut Y pulls on the cable?

A student is tasked with using a force table to balance a small ring in the center of a pin, as shown in Figure 1. For each of the four strings shown, one end is attached to the small ring, and the other end is attached to a hanger that can hold masses. Each string is wrapped around a pulley so that the hanger and masses are at rest. The location of each pulley may be changed. Figure 2 shows a top-down view of the free-body diagram of the forces exerted on the pin at a particular moment in time. From a top-down perspective, in what direction will the pin accelerate?

Up and to the left

Which of the following experiments could be used to determine the inertial mass of a block?

Use a spring scale to exert a force on the block. Measure the acceleration of the block and the applied force.

A student wants to launch a toy dart toward a target that hangs from a light string. At time t=0, the dart is launched with an initial speed v0 at an angle θ0 above the horizontal ground. At the instant the dart is launched, the string is cut such that the target begins to fall straight down. The positive horizontal direction is considered to be to the right, and the positive vertical direction is considered to be up.

Vertical, Vertical

The amusement park ride shown above takes riders straight up a tall tower and then releases an apparatus holding seats. This apparatus free-falls back to Earth and is stopped safely right above the ground. Which of the following indicates the magnitude of the gravitational force exerted on a rider of mass m on the way up and on the way down?

Way Up:Equal to mg, Way Down:Equal to mg

The force diagram above shows a box accelerating to the right on a horizontal surface of negligible friction. The tension T is exerted at an angle of 30° above the horizontal. If μ is the coefficient of kinetic friction between the box and the surface, which of the following is a correct mathematical equation derived by applying Newton's second law to the box?

a=Tcos(θ)−μ(Mg−Tsin(θ))/M

In the setup shown in the figure, two blocks of equal mass M are at rest but are just about to slip. Also shown is a free-body diagram for the block on top of the table. In this setup, the coefficient of static friction between the table and the block resting upon it must be

at least 1.0

hree boxes are pulled to the left by strings with negligible mass on a horizontal surface, as shown above. The masses of the boxes are m1, m2, and m3, where m3>m2>m1. Friction between the boxes and the surface is negligible. The figure below shows force diagrams for each box. A student is trying to determine the tensions in the strings connecting the boxes. If the acceleration of the system and the pulling force F are known, which of the following pairs of equations could be used to find the tensions?

m3a3=TB and m2a2=TA−TB

An object of mass m is initially at rest and free to move without friction in any direction in the xy-plane. A constant net force of magnitude F directed in the +x direction acts on the object for 1 s. Immediately thereafter a constant net force of the same magnitude F directed in the +y direction acts on the object for 1 s. After this, no forces act on the object. Which of the following vectors could represent the velocity of the object at the end of 3 s, assuming the scales on the x and y axes are equal?

starts a (0,0) has a slope of 1

A student stands at one end of a raft floating in a pool with equally spaced marks along the bottom, as shown above. The student and the raft have the same mass. The student walks to the opposite end of the raft. Which of the following best shows the final locations of the raft and student relative to the marks at the bottom of the pool? Assume that there is no drag force between the raft and the water.

the student is standing at the front of the raft where the raft is at the same spot

Two identical blocks, block A and block B, are placed on different horizontal surfaces. Block A is initially at rest on a smooth surface, while block B is initially at rest on a rough surface. A constant horizontal force of magnitude F0 is exerted on each block. After the force has been applied for a time Δt, the speeds of blocks A and B are vA and vB, respectively. Which of the following claims indicates the correct relation between vA and vB and provides the best justification for the relation?

vA>vB. The forces between the atoms in a block and the atoms in a surface oppose the motion of the block and are greater, on average, for block B.

A block slides with constant velocity down a rough inclined plane that makes an angle of θ with the horizontal. It experiences three forces: gravitational (Fg), normal (FN), and frictional (Ff). Which of the following gives the magnitude of the net force on the block?

zero