AP Physics 1 - Final Exam 23'24'
A 100 kg cart goes around the inside of a vertical loop of a roller coaster. The radius of the loop is 3 m and the cart moves at a speed of 6 m/s at the top. The force exerted by the track on the cart at the top of the loop is
200 N
A car with speed v and an identical car with speed 2v both travel the same circular section of an unbanked road. If the frictional force required to keep the faster car on the road without skidding is F, then the frictional force required to keep the slower car on the road without skidding is
F/4
A student swings a ball on a light rod at a constant speed in a vertical circle, as shown in the figure. Which of the following correctly ranks the magnitudes of the forces exerted by the rod on the ball F1, F2, F3, and F4 when the ball is at locations 1, 2, 3, and 4, respectively?
(F2 = F3) > F4 > F1 Correct. The circular motion of the ball is a result of the two forces acting on the ball: the force of gravity exerted on the ball and the force exerted by the rod on the ball. The radial component of the vector sum of those forces causes the centripetal acceleration of the ball. The radius of the circular path and the speed of the ball is constant, so the centripetal acceleration is constant. The force exerted by the rod on the ball is always directed towards the center of the circle, and the force of gravity is always directed vertically downwards. When the ball is near the top of the circle, the force of gravity contributes to the centripetal acceleration of the ball, and the force of the rod on the ball decreases, resulting in a centripetal acceleration. When the ball is near the bottom of the circle, the rod must support the weight of the ball and as well as cause the ball to move in a circular path with the same centripetal acceleration, causing the force of the rod on the ball to increase. At points 2 and 3, the force of the rod on the ball is equal and the largest of the nearest points because the points are closest to the bottom of the circular path. The force of the rod on the ball is equal at these two points because they are equidistant from the bottom of the circular path. The force of the rod on the ball at point 1 is the least of the labeled points because it is the closest point to the top of the circular path.
Box A of mass m sits on the floor of an elevator, with box B of mass 2m on top of it, as shown in the figure above. The elevator is moving upward and slowing down. FA is the magnitude of the force exerted on box A by box B, FB is the magnitude of the force exerted on box B by box A, and Fg is the magnitude of the gravitational force exerted on box B. Which of the following ranks the forces in order of increasing magnitude?
(FB = FA) < Fg
Three identical rocks are launched with identical speeds from the top of a platform of height 0 h . The rocks are launched in the directions indicated above. Which of the following correctly relates the magnitude vy of the vertical component of the velocity of each rock immediately before it hits the ground?
(vy1 = vy2) > vy3
A box of mass m slides up a ramp with initial velocity +v0. The kinetic friction force on the box has magnitude f. Which of the following is a correct equation that could be used to determine the acceleration a of the box?
-f - mg sin theta = ma Correct. The frictional force is exerted by the ramp in the -x direction, and the component of the gravitational force also points down the ramp in the -x direction. It is the sum of these two that can be used to determine the acceleration of the box.
One end of a string is attached to the ceiling and the other end is attached to a small sphere traveling in a circular path, as shown above, with a constant speed of 1m/s. The string makes an angle of 30° to the vertical. If the tension in the string is 6N and the circumference of the circle is 1m, how much work is done on the sphere by the string as the sphere travels through one revolution? `
0 J Correct. The net force acting on the sphere is directed radially toward the center of circular trajectory of the sphere. The work done on the sphere can be determined by the following equation: W sphere=Fspheres sphere cos(theta) , where Fsphere is the net force exerted on the sphere, s spehre is the path along which the sphere moves, and theta is the angle between the net force applied to the sphere and the path that the sphere travels along. The angle between the force exerted on the sphere and its path is always 90° , so the associated work done on the sphere is Wsphere= Fsphere ssphere cos(90°)=0 .
A toy doll and a toy robot are standing on a frictionless surface facing each other. The doll has a mass of 0.20 kg, and the robot has a mass of 0.30 kg. The robot pushes on the doll with a force of 0.30 N. The magnitude of the acceleration of the robot
1.0 m/s^2 Correct. According to Newton's third law of motion, if object A exerts a force on object B, then object B exerts a force of equal magnitude but opposite direction on object A. Therefore, if the robot pushes the doll with a force of 0.3 N, the doll exerts a force on the robot of 0.3 N. Newton's second law of motion can then be used to calculate the robot's acceleration.
Two blocks of masses 1.0 kg and 2.0 kg, respectively, are pushed by a constant applied force F across a horizontal frictionless table with constant acceleration such that the blocks remain in contact with each other, as shown above. The 1.0 kg block pushes the 2.0 kg block with a force of 2.0 N. The acceleration of the two blocks is
1.0 m/s^2 F = ma
An amusement park ride consists of a large vertical wheel of radius R that rotates counterclockwise on a horizontal axis through its center, as shown above. The cars on the wheel move at a constant speed v. Points A and D represent the position of a car at the highest and lowest point of the ride, respectively. A person of weight Fg sits upright on a seat in one of the cars. As the seat passes point A, the seat exerts a normal force with magnitude 0.8Fg on the person. While passing point A, the person releases a small rock of mass m, which falls to the ground without hitting anything. What is the normal force exerted on the rider when passing point D?
1.2 Fg Correct. Since the rider is undergoing uniform circular motion, the net force on the rider is a force of constant magnitude Fc that is always directed toward the center of the rider's circular path.At point A, taking the downward direction to be positive, Fc is found to be Fc = ΣF = Fg−FnA=Fg−0.8Fg=0.2Fg.At point D, this time taking the upward direction to be positive, Fc = ΣF = FnD−Fg. Solving this equation for the normal force at point D gives FnD = Fc+Fg=0.2Fg+Fg=1.2Fg.
On Earth, when a box slides across a horizontal board, the board exerts a frictional force of magnitude �0 on the box. The board and the box are moved to a planet with twice the radius but one-third the mass of Earth. When the box slides across the board, the frictional force exerted by the board on the box is now
1/12 F initial Correct. The frictional force between the board and the box is proportional to the normal force exerted on the box by the board. The board is horizontal and the box does not accelerate vertically, so the normal force is equal to the weight of the box. A planet that has twice the radius and one-third the mass of Earth will exert a gravitational force on the box equal to: Since the weight of the box on the new planet is 1/12 of the weight of the box on Earth, the frictional force exerted by the board on the box on the new planet is 1/12 of the frictional force exerted by the board on the box on Earth.
A board is hung from two springs, as shown in the figure above, with the board in equilibrium. Each spring has a spring constant of 10,000 N/m. How far will each spring stretch when a person of mass 50 kg sits on the board and the board again comes to equilibrium?
1/40 m
A meteoroid is in a circular orbit 600 km above the surface of a distant planet. The planet has the same mass as Earth but has a radius that is 90 % of Earth's (where Earth's radius is approximately 6370 km).
10 m/s^2 towards the center of the planet Correct. The meteoroid's acceleration must be in the same direction as the net force exerted on the meteoroid. The net force is entirely due to the gravitational force exerted by the planet, which is toward the center of the planet. Newton's law of universal gravitation can be used to determine the magnitude of the meteoroid's acceleration. First, note that the distance from the meteoroid to the planet's center is (0.9×6370+600) km=6333 km, which is very nearly (99.4% of) the radius of Earth. The gravitational force on the meteoroid is then Fg=Gm1m2/r2≈G mEarth mmeteoroid/rEarth2. Dividing by the mass of the meteoroid gives an acceleration for the meteoroid of ameteoroid=Fg mmeteoroid≈G mEarth/rEarth2= g≈10 ms2.
An object is moving to the west at a constant speed. Three forces are exerted on the object. One force is 10 N directed due north, and another is 10 N directed due west. What is the magnitude and direction of the third force if the object is to continue moving to the west at a constant speed?
10√2 N , directed southeast
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
12,000 N
On another planet, a ball is in free fall after being released from rest at time t=0. A graph of the height of the ball above the planet's surface as a function of time t is shown. The acceleration due to gravity on the planet is most nearly
16 m/s^2 Correct. The free fall acceleration close to the surface of any planet can be treated as constant, and so the magnitude of the acceleration can be determined by using the data given in the graph. y = y initial + velovity y initial * time + 0.5 * a * t^2
The graph above shows the speed of a truck as it moves along a straight, level road. How far does the truck travel in the 10s time interval shown?
180 m Correct. The distance traveled equals the area under the graph between t=0s and t=10s. That total area consists of a rectangle between a speed of 0 and a speed of 6m/s, with area 60m, and a triangle between a speed of 6m/s and a speed of 30m/s, with area 120m. Adding those two parts of the area under the graph gives the total area of 180m.
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 COFk Mg cos θ
Planet X has twice Earth's mass and three times Earth's radius. The magnitude of the gravitational field near Planet X's surface is most nearly
2 N/kg 3^2 = 9 2/9 * 9.8 = close to 2
A student sets an object attached to a spring into oscillatory motion and uses a position sensor to record the displacement of the object from equilibrium as a function of time. A portion of the recorded data is shown in the figure above. The total distance traveled by the object between 0.35 s and 0.40 s is most nearly
2 cm
A student throws a rock horizontally from the edge of a cliff that is 20 m high. The rock has an initial speed of 10 m/s. If air resistance is negligible, the distance from the base of the cliff to where the rock hits the level ground below the cliff is most nearly
20 m
A distant planet has an acceleration due to gravity of 4 m/s2 near its surface. An object is released from rest from the top of a tall cliff on the planet, and the object lands at the bottom of the cliff in 20 seconds. A second object is then thrown upward from the edge of the same cliff with a speed of 4 m/s. The time it takes the second object to reach the bottom of the cliff is most nearly
21 s Correct. With a gravitational acceleration of 4 m/s^2 and an initial speed of 4 m/s, the second object takes one second to come instantaneously to rest and reach its maximum height. During this time its average speed is half of 4 m/s, or 2 m/s, so during the one-second interval it reaches a height of 2 meters above where it was thrown. It then falls from rest from the 2 meter height, and after 20 more seconds it drops the same distance that the first object dropped and is 2 meters above the ground, traveling downward at (4 m/s^2)(20 s)=80 m/s. At this speed, it takes a small fraction of one second to reach the ground. The total time is then very nearly 1 s+20 s, or 21 s.
At time t=0s, an object is moving to the right with a velocity v that can be modeled by the equation v=(4.2 m/s)-(1.4 m/s2)t. At what time, if any, does the object change its direction of motion?
3.0 s Correct. Comparing the original equation to the kinematic equation of motion: It can be determined that the initial velocity of the object is positive 4.2m/s and the acceleration is −1.4 m/s^2. Any time the velocity and acceleration are in opposite directions, the object is slowing down. Since the acceleration is constant, it will slow down, instantaneously come to rest and then reverse direction. So the moment that it begins to travel in the opposite direction is when the velocity of the object is equal to zero. Setting vf equal to zero: Vx = v^2 x0 + at
Four different constant forces are exerted on a 2.0 kg object. The figure represents the magnitude and direction of each force. If the object is initially at rest, how long will it take the object to reach a speed of 2.0 m/s?
4.0 s Correct. Summing the forces in the vertical direction shows that the object is not accelerating in the vertical direction. Summing the forces in the horizontal direction shows that the object is accelerating in the horizontal direction. The object starts from rest, so to find the time it takes the object to accelerate to 2.0m/s, a kinematic equation can be used.
The total change in the object's speed between 1.0 s and 1.1 s is most nearly
5 cm / s
A block is projected up a frictionless plane with an initial speed vo. The plane is inclined 30° above the horizontal. What is the approximate acceleration of the block at the instant that it reaches its highest point on the inclined plane?
5 m/s^2 down the incline 9.8 x sin(30)
An engineer measures the velocity v of a remote-controlled cart on a straight track at regular time intervals. The data are shown in the graph above. During which of the following time intervals did the cart return to its position at time t=0 s ?
7s less than or equal to t less than 10s Correct. When given a graph of a system's velocity as a function of time, the area bound between the curve and the horizontal axis is equal to the displacement of the object for the time interval under consideration.From 0 s to approximately 3.0 s, the area bound by the best-fit curve and the horizontal axis is positive. This means that the remote-controlled car has been displaced in the positive direction during this time interval.At approximately 3.0 s, the speed of the remote-controlled car becomes zero. At approximately 5.0 s, the car begins to increase its speed in the negative direction. Therefore, the remote-controlled car has reversed its direction.When the area bound by the best-fit curve and the horizontal axis is negative and equal in magnitude to the positive area from 0 s to approximately 3.0 s, the remote-controlled car will return to its original position. This will occur over the time range 7s ≤ t < 10 s.
At time t=0, a cart is at x=10 m and has a velocity of 3 m/s in the −x -direction. The cart has a constant acceleration in the +x -direction with magnitude 3 m/s^2 < a <6 m/s^2 . Which of the following gives the possible range of the position of the cart at t=1 s ?
8.5m < x < 10m
A stone disk is sliding on frictionless ice to the west with speed v, as shown in the figure above. As the disk slides by, a child uses a rubber mallet to hit the disk at point X, exerting a force directly toward the center of the disk. The child hits point X every half second for about 10 s, changing the trajectory of the disk but not causing it to rotate. Which of the following most closely approximates the path of the disk while the child is hitting it?
A parabolic path
A meterstick is held as shown above and then released from rest. The tabletop has negligible friction. Which figure below best indicates the path of the center of mass of the meterstick as it falls?
Arrow pointing straight down
The figure shows three cases where two spheres are touching and attract each other with the gravitational force. The radii of the spheres in each case are shown. All of the spheres are made of material with the same density. Which of the following correctly ranks these cases based on the gravitational force between the spheres?
B > C > A Correct. The planets all have the same density, so the mass of each planet is related to the radius of the planet cubed.
An object begins at position x = 0 and moves one-dimensionally along the x-axis with a velocity v expressed as a function of time t according to the graph above. At what time does the object pass through x = 0 again?
Between 20s and 30s
A box of mass m slides a distance d down a rough incline from an initial height ℎ, as shown in the figure above. The surface of the incline has a coefficient of kinetic friction COF and makes an angle theta with the horizontal. How much mechanical energy is dissipated as the box slides to the bottom of the incline?
COFdmg cos theta Correct. The frictional force Ff is in the opposite direction to the direction of motion, so the frictional force dissipates an amount of energy equal to Ff d. The kinetic frictional force is defined to be Ff = COF N = COF mg cos theta, where N is the normal force, and is equal to the component of the gravitational force perpendicular to the surface of the incline. Therefore, the energy dissipated by friction is COF dmg cos theta.
Blocks 1 and 2 are connected by a light string that passes over a pulley with negligible mass and friction, as shown in the figure. Block 1 is on a table covered with two different materials, A and B. The two-block system is released from rest, and the speed of block 1 begins to increase. When block 1 reaches material B, its speed increases at a greater rate. Which of the following correctly compares the coefficient of kinetic friction COF between block 1 and the two materials and describes the change in the magnitude of the net force on block 2 as block 1 slides from material A to material B?
Coefficients - COF a > COF b Net Force - Increases Correct. The prompt states that when block 1 reaches material B, its speed increases at a greater rate. This means that the acceleration of block B is larger when it is on material B than it is when block B is on material A. For the acceleration of block B to be larger, there must be a larger net force exerted on the block, therefore the net force must have increased. For the net force to increase, the frictional force must have decreased, meaning that the coefficient of friction between block B and material B must be smaller than the coefficient of friction between block B and material A. COF a > COF b
Which of the following graphs could describe the motion of the two boxes as they are moved across the room?
Correct - Scenario 2 up Scenario 1 Constant Correct. The component of F0 in the horizontal direction is identical in both scenarios, however, in scenario 1 the student is applying an additional component of F0 downward, which increases the normal force exerted by the ground on the box, which also increases the frictional force between the ground and the box. In scenario 2, the student exerts that same component of F0 vertically upward, which reduces the normal force exerted by the ground on the box and the frictional force on the box. The acceleration of the box in scenario 2 will be greater than the acceleration of the box in scenario 1. The magnitude of the acceleration of the box is represented by the slope of the speed vs. time graphs. The graphs in choice C show that acceleration in scenario 2 is greater than the acceleration of the box in scenario 1 and that the box remains at a constant speed in scenario 1. For the box to move with constant speed in scenario 1, the horizontal components of the forces must sum to zero. If the forces were balanced in scenario 1, they cannot be balanced in scenario 2 where the horizontal component of �0 remains constant while the frictional force decreases. So the box in scenario 2 will have a non-zero acceleration.
At which of the following times do the two objects have the same velocity?
Correct Answer tC Correct. The slope of a line tangent to the graph of position as a function of time is equal to the velocity of the object. The time at which the slope of the lines tangent to their respective position vs. time graphs are equal is at time tC.
Two identical cars, car 1 and car 2, are moving in opposite directions on a straight road. The position of each car as a function of time is represented in the graph. What is the speed of the center of mass of the two-car system?
Correct answer - Zero Correct. The cars are identical, and so have identical masses. The velocity of each car can be determined from the slope of the position vs. time graph. The velocity of car 1 is equal to (30m/s-10ms1.0 s)=+20m/s. The velocity of car 2 is (-10m/s-10m/s1.0 s)=−20m/s. The cars are identical and are moving at the same speeds and in opposite directions, so the speed of the center of mass is equal to zero.
Block 1 slides rightward on the floor toward an ideal spring attached to block 2, as shown. At time t1, block 1 reaches the spring and starts compressing it as block 2 also starts to slide to the right. At a later time, t2, block 1 loses contact with the spring. Both blocks slide with negligible friction. Taking rightward as positive, which pair of graphs could represent the acceleration of block 2 and the center-of-mass acceleration of the two-block system?
Correct. Between t1 and t2, there is a net force on block 2 exerted from the spring, because block 1 collides with and compresses the spring. This causes a rightward acceleration that increases and returns to zero as the spring compresses and returns to its original length during the time t1 to t2. There are no external forces acting on the blocks-spring system, so the center of mass of the two-block system during the time t1 to t2.
Three blocks are pushed along a rough surface by a force with magnitude P, as shown above. Fc is the magnitude of the contact force between blocks 2 and 3, and Ff, Fn, and Fg are the magnitudes of the friction, normal, and gravitational forces on block 3, respectively. Which of the following is a correct free-body diagram for block 3?
Correct. Block 2 pushes on block 3 by exerting the contact force of magnitude Fc toward the right. The friction force of magnitude Ff will then be in the opposite direction, or toward the left. The gravitational force FG is exerted by Earth downward on block 3. To balance the downward gravitational force, the surface pushes upward on block 3 with a normal force of magnitude Fn.
The graph shows the force exerted on a ball by the floor as a function of time as the ball bounces off the floor. If the positive direction is upward, which of the following graphs could represent the force exerted on the floor by the ball?
Correct. Newton's third law states that the force exerted by the floor on the ball is equal in magnitude and opposite in direction to the force exerted by the ball on the floor.
Two students need to move two identical boxes of mass M0 across a room where friction between the floor and the boxes cannot be neglected. One student moves the first box by pushing with a force of magnitude F0 at an angle theta from the horizontal, as shown in the figure for scenario 1. The other student moves the second box by pulling with a force of magnitude F0 at the same angle theta from the horizontal, as shown in the figure for scenario 2. Which of the following is a correct expression for the acceleration of the box in scenario 2 ?
Correct. The acceleration of the box can be determined by using Newton's second law analysis in vertical and horizontal components:
At time t=0, a projectile is launched from the top of a cliff at an angle of 30 degrees below the horizontal. Which of the following pairs of graphs best represents the horizontal displacement Δx and the vertical velocity component v vert of the projectile as a function of time t?
Correct. The acceleration of the projectile is vertically downward. Therefore, the horizontal velocity component is constant and, in this case, nonzero. Since the horizontal velocity component is a nonzero constant, the graph of the horizontal displacement is a straight line with a nonzero slope, as depicted in the graph on the left. The downward acceleration means that the graph of the vertical velocity component is a straight line with a nonzero slope. Moreover, since the projectile is launched at a 30 degree angle below the horizontal, v vert is initially nonzero, as depicted in the graph on the right.
A block is attached to the end of a string and initially moves at a constant speed in a horizontal circle of constant radius, as shown. The radius is then increased slowly while the speed remains the same. Which of the following graphs best represents the force exerted on the block by the string as a function of the radius?
Correct. The centripetal force exerted on the block is related to the radius of the circle made by the block by: Fc=mv^2/R, so the centripetal force is inversely proportional to 1/R, as shown in this graph.
Carts 1 and 2 are initially moving toward each other, as shown in the top figure. The carts collide and afterward are both moving to the right, as shown in the bottom figure. If the positive direction is to the right, which of the following best represents the force exerted on each cart by the other during the collision as a function of time?
Correct. The forces that cart 1 exerts on cart 2, and the forces that cart 2 exerts on cart 1 are a Newton's third law pair and are equal in magnitude and opposite in direction. Since cart 1 is initially moving to the right, cart 1 will exert a force that is in the positive direction on cart 2, and cart 2 will exert a force on cart 1 that is in the negative direction.
An object is subject to multiple forces that result in the object having horizontal and vertical velocity components Vx and Vy, respectively as a function of time, as shown. Which of the following free-body diagrams could represent the forces exerted on the object?
Correct. The horizontal velocity is constant, which means that the horizontal acceleration is zero. Because the horizontal acceleration is zero, the horizontal component of the net force must be equal to zero. The slope of the vertical velocity as a function of time is negative, which means that the acceleration is negative and the vertical component of the net force must be negative. In this free body diagram, the sum of the horizontal components is zero, and the sum of the vertical components is negative.
A disk of mass m slides with negligible friction to the right with speed vi on a horizontal table. The disk collides elastically with a uniform rod of length ℓ that is at rest and free to pivot about one end, as shown in Figure 1 above. The disk rebounds to the left with speed vf, and the rod rotates with friction and stops at a final angle theta f from its initial position, as shown in Figure 2. Which of the following describes the direction of the forces exerted by the disk and rod on each other during the collision?
Direction of Force Exerted on Disk by Rod - To the left Direction of Force Exterted on Rod by Disk - To the right Correct. According to Newton's third law, when two objects exert forces on one another, the forces are equal in magnitude and opposite in direction.
A vertical spring launcher is attached to the top of a block and a ball is placed in the launcher, as shown in the figure. While the block slides at constant speed to the right across a horizontal surface with negligible friction between the block and the surface, the ball is launched upward. When the ball reaches its maximum height, what will be the position of the ball relative to the spring launcher?
Directly above the spring launcher Correct. When the ball is in the launcher, it travels with the launcher and has the same horizontal speed as the block and launcher. There is no net horizontal force on either the ball or the launcher-block system, so the horizontal speed of both the ball and launcher-block does not change. As the ball rises and reaches the maximum height, both the ball and launcher-block continue forward at the same speed, so the ball is still directly over the launcher.
The figure above represents the orbits of two planets of equal mass that orbit their star in the counterclockwise direction as a double-planet system. From the point of view of an observer on either planet, the planets appear to orbit each other while also orbiting the star. The dots on the orbits represent the position of the planets at time t0, and X is the position of their center of mass at that time. Which of the following arrows best represents the acceleration of the center of mass of the double-planet system when it is at point X ?
Down and to the left
A hollow plastic ball is projected into the air. There is significant air resistance opposing the ball's motion, so the magnitude of the ball's acceleration is not equal to g. At time t, the ball is moving up and to the right at an angle of 45° to the horizontal, as shown above. Which of the following best shows the magnitude a and the direction of the ball's acceleration at time t ?
Down and to the left, a > g
An elevator carrying a person of mass m is moving upward and slowing down. How does the magnitude F of the force exerted on the person by the elevator floor compare with the magnitude mg of the gravitational force?
F < mg
Three blocks, A, B, and C, are pushed by a constant force F that is applied on block A as shown. There is negligible friction between the blocks and the surface. When a small object is attached to the top of block B, the normal force between blocks A and B is F AB and the normal force between blocks B and C is F BC. How will the values of F AB and F BC change if the small object is moved to the top of block C and the experiment is repeated?
F AB - Stays the same F BC - Increases Correct. The net force on the system of three blocks is the same in both situations, so the acceleration of each block is equal to the acceleration of the system which is equal regardless of which blocks the object is attached to.Block A has two horizontal forces exerted on it, force F, which does not change, and the force exerted on A from B. The acceleration of A remains constant between the two situations, which means the net force exerted on A is the same between situations. The force exerted by block B on block A must stay the same.Block C has only one horizontal force exerted on it, which is the force from block B exerted on block C. Since the acceleration of block C remains constant, but the mass of block C increases when the small object is attached to it, the net force on C must also increase. The force exerted by block B on block C must increase.
A box of mass m is on a rough inclined plane that is at an angle θ with the horizontal. A force of magnitude F at an angle Φ with the plane is exerted on the block, as shown above. As the block moves up the plane, there is a frictional force between the box and the plane of magnitude f. What is the magnitude of the net force acting on the box?
F cosΦ - mg sin θ - f
Block A and block B move toward each other on a level frictionless track. Block A has mass m and velocity +v . Block B has mass 2m and velocity -v . The blocks collide, and during the collision the magnitude of the net force exerted on block A is F. What is the magnitude of the net force exerted on block B, and why does it have that value?
F, because the net force is equal to the mutual contact force between the blocks.
The incomplete data in the table above were recorded during an experiment in which two carts on a frictionless one-dimensional track collided head-on. What are the magnitudes of the average force F2 exerted on cart 2 and the average acceleration a2 of cart 2 during the collision?
F2 - 30N a2 - 60 m/s^2 Correct. The key insight here stems from Newton's third law: since cart 2 exerts a 30N force on cart 1, cart 1 also exerts a 30N force on cart 2. But that does not mean the two carts have the same acceleration. Cart 2 is lighter, so it accelerates more than cart 1 when subjected to a given force. More precisely, since a =F/m, and since cart 2 has a smaller mass m, it therefore acquires a bigger acceleration than cart 1 does: a2=F2/m2=30N/0.5kg=60m/s2.
Two astronauts are connected by a taut cable and are initially at rest with respect to a nearby space station. Astronaut X throws a large container to Astronaut Y. Figure 1 above shows the astronauts immediately after the container is thrown by Astronaut X, and Figure 2 shows the astronauts immediately after the container is caught by Astronaut Y. Which of the following describes the motion of Astronaut Y in Figures 1 and 2 ?
Figure 1 - Moves to the left Figure 2 - does not move
The figures show a cart moving over the top of a hill (Case 1), moving at the bottom of a dip (Case 2), and moving at the top of a vertical loop (Case 3). In each case, the normal force acting on the car is Fn and the weight of the car is Fg. In which case is it always true that Fn>Fg, and in which case is it always true that Fn<Fg?
Fn > Fg Always Fn<Fg Always Case 2 Case 1 Correct. In case 2, since the cart is moving through the bottom of the dip, the cart is accelerating directly upward at the bottom. This means that the net force must be upward, and so Fn>mg. In case 1, since the cart is over the top of the hill, the cart is accelerating toward the center of the circle, which is directly downward. Since the acceleration is downward, the net force is downward, which means that Fn>mg. In case 3, the normal force could be greater than or less than the weight of the cart, depending on the speed of the cart.
A cart of mass m rolls past the circular bottom of a hill (point P). Which of the following statements about the normal force Fn exerted on the cart at point P is correct?
Fn is greater than mg at point P, because the cart is experiencing an upward acceleration. Correct. There are two forces exerted on the cart at point P, the gravitational force, which is exerted vertically downwards and the normal force from the track, which at point P is exerted vertically upwards. At point P the cart is moving along a circular path, and so is accelerating towards the center of that circular path. The acceleration of the cart must be directed upwards, and so the net force must be vertically upward. The net force can only be upwards if the normal force from the track is larger than the weight.
Blocks X and Y are glued together and released from rest on a ramp with negligible friction, as shown in trial 1. The blocks are then separated and connected by a light spring, as shown in trial 2. The spring is compressed and the blocks are again released from rest on the ramp. Immediately after the blocks are released, is the net force on the two-block system the same or different between trial 1 and trial 2? Immediately after the blocks are released, is the net force on block Y the same or different between trial 1 and trial 2?
Force on System - Same Force on Block Y - Different Correct. In trial 2, the force that the spring exerts on block X is equal and opposite to the force that the spring exerts on block Y. Therefore, the net force exerted by the spring on the system is zero. So, the net force exerted on the system in trial 1 and 2 is the same. However, in trial 2, when analyzing only block Y, there is the additional force exerted on the block by the spring, so the net force on block Y is different in trial 2.
In a classroom at time t = 0 , a sphere is thrown upward at a 45° angle to the horizontal. At time t1, while the sphere is still rising, it bounces off the ceiling elastically and with no friction. Which of the following pairs of graphs could represent the sphere's horizontal velocity and vertical velocity as functions of time t?
Horizontal - Positive Constant Line Vertical - Positive then down with straight vertical line in the middle
A box of mass m is released from rest and accelerates down a ramp that is at an angle theta to the horizontal, as shown. The coefficient of kinetic friction between the box and the ramp is COF. As the box is sliding down the ramp, how are the magnitudes of the horizontal and vertical components of the box's velocity changing, if at all?
Horizontal Component - Increasing Vertical Component - Increasing Correct. The box is accelerating down the ramp, so the acceleration vector has components in both the horizontal and the vertical directions. Since the box is released from rest, the velocity is increasing in both the vertical and horizontal directions.
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 - T1 cos theta1 Vertical Component - mg - T1 sin theta1
The toy car shown in the figure above enters the vertical circular loop with an initial velocity and moves completely around the loop without friction. If the car has no means of self-propulsion, which of the following is true of the car's acceleration at the instant it is at point P ?
It has components both downward and toward the center of the circle.
Two blocks of masses m and M are suspended as shown above by strings of negligible mass. If a person holding the upper string lowers the blocks so that they have a constant downward acceleration a, the tension in the string at point P is
M (g -a )
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 at rest on section 1 of the incline, what is the magnitude of the force of static friction exerted on the block by the incline?
Mg sin θ
A blue sphere and a red sphere with the same diameter are released from rest at the top of a ramp. The red sphere takes a longer time to reach the bottom of the ramp. The spheres are then rolled off a horizontal table at the same time with the same speed and fall freely to the floor. Which sphere reaches the floor first?
Neither; the spheres reach the floor at the same time. (Because Same high)
In Figure 1, cart Y is connected to cart X by a tight string and is also connected to the hanging block of mass m0 by a light string that passes over a pulley. Figure 2 shows a system that is identical except for one change: cart Y and X are connected by a spring at its equilibrium length. Both systems are released from rest. Is the hanging block's acceleration as a function of time the same in both systems, and why or why not?
No, because the tension in the string connected to the block is constant in one system but not in the other. Correct. The net force on the system is constant, so the acceleration of the center of mass of each system is the same. However, the net force on each individual piece of the system can be different between the two systems. In case 1 the acceleration of the system and of each object in the system is equal because the string is assumed to be ideal and so will not stretch.When the string is replaced with the spring, the spring stretches, exerting a changing force on cart X and changing the tension in the string supporting the block Y. The changing net force on each individual cart results in their respective accelerations being different in each system, even though the acceleration of the center of mass of each system is the same.
A block moving to the right on a level surface with friction is pulled by an increasing horizontal force also directed to the right. As the applied force increases, which of the following is true of the normal force and the frictional force on the block?
Normal Force - Reamins Constant Frictional Force - Remains Constant
The position as a function of time for two objects moving along a straight line is shown in the graph. Which statement is true about the distances the two object have traveled at time t?
Object 1 has traveled a grater distance. Correct. The graph shows the position of each object as a function of time. Since object 1 is at the same position at tF, as object 2 was in at time tA. The two objects have the same displacement. However, object 1 travels a longer distance as it goes backwards and forwards during the time between tA and tF
At time t = 0 two figure skaters are moving together over ice with negligible friction, as shown above. Skater 1, represented by the large black dot, is twice as massive as skater 2, represented by the gray dot. At t = 2 s the skaters push off of one another. The location of skater 1 is shown at t = 4 s . At t = 4 s , skater 2 is located at which of the labeled points?
Point D
The figure above shows a truck pulling three crates across a rough road. Which of the following shows the directions of all the horizontal forces acting on crate 2 ?
Rope <------- Crate 3 <------- -------> Cable Friction <-------
The position and velocity of a car moving along a straight road are recorded as functions of time, as shown in the graphs above. Which of the following correctly describes the car's speed and acceleration?
Speed - Decreasing Acceleration - Positive Correct. The speed is the magnitude of the velocity. The car starts out moving at speed 15m/s, and the speed decreases until it reaches zero around 3s. However, the acceleration of the car is positive because the acceleration is the rate of change of velocity. The velocity is changing in the positive direction, indicated by the positive slope of the velocity graph.
Planet 1 orbits Star 1 and Planet 2 orbits Star 2 in circular orbits of the same radius. However, the orbital period of Planet 1 is longer than the orbital period of Planet 2. What could explain this?
Star 1 has less mass than Star 2.
A projectile launched from a cliff at time t=0 follows the path indicated by the dashed line in the above figure. The axes indicate the positive horizontal and vertical directions. Which of the following graphs could represent the projectile's motion?
Straight down away from zero and constant
Two identical blocks A and B are connected by a lightweight rope. Block A is pulled to the right by a constant force F0. The blocks are moving to the right across a rough surface and approach point P, where the rough surface transitions to a surface with negligible friction. How does the tension, T, in the rope connecting the blocks change, if at all, as block A passes point P?
T increases Correct. As block A passes point P, the net force on the block A - block B system increases because there is no longer a frictional force exerted on block A from the surface. Because the net force on the system increases, the acceleration of the system must also increase. Looking at block B only, there are only two horizontal forces, the force of tension and the frictional force. Since the frictional force remains constant on block B, but the acceleration of block B increases, the force of tension exerted on block B must also increase.
A kitten sits in a lightweight basket near the edge of a table. A person accidentally knocks the basket off the table. As the kitten and basket fall, the kitten rolls, turns, kicks, and catches the basket in its claws. The basket lands on the floor with the kitten safely inside. If air resistance is negligible, what is the acceleration of the kitten-basket system while the kitten and basket are in midair?
The acceleration is directed downward with magnitude equal to g because the system is a projectile.
A launcher with mass m1 is suspended from the ceiling by a string, as shown. A block with mass m2 < m1 is launched horizontally. At the moment of launch, the block has unknown speed v2 and the launcher has unknown speed v1 in the opposite direction. Which of the following is a true statement about the forces exerted between the launcher and block?
The block and the launcher exert forces of equal magnitude on each other. Correct. The block and the launcher exert forces of equal magnitude on each other that are opposite in direction per Newton's third law.
A small cart is rolling freely on an inclined ramp with a constant acceleration of 0.50 m/s^2 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 s?
The cart is traveling in the -x-direction and is speeding up.
Two objects, A and B, move toward one another. Object A has twice the mass and half the speed of object B. Which of the following describes the forces the objects exert on each other when they collide and provides the best explanation?
The forces exerted by each object on the other are the same, because interacting objects cannot exert forces of different magnitude on each other.
A person stands in an elevator. The elevator starts from rest and travels from the first floor to the fifth floor of the building. Which of the following forces has a magnitude equal to the person's weight during the entire elevator ride?
The gravitational force exerted by the person on Earth Correct. According to Newton's third law, the gravitational force exerted by the person on Earth is equal in magnitude to the gravitational force exerted by Earth on the person. The person's weight does not change as the elevator moves from the first to fifth floor.
Each of the figures above shows a tractor attached to an object. The tractor exerts the same constant force F on each object in every case. Which of the following is a true statement about an object and the relative magnitude of the force exerted by the object on the tractor?
The magnitude of the force exerted by each object on the tractor is equal, because the tractor exerts an equal force on each object.
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
The motion of an object is shown in the velocity-time graph. Which best describes the motion of the object?
The object travels in the same direction for the entire time. Correct. During the time interval shown, the velocity increases, is constant, and then decreases. However, the velocity of the object is always positive which indicates the object is always moving in the positive direction.
An object's velocity v as a function of time t is given in the graph above. Which of the following statements is true about the motion of the object?
The object's initial and final positions are the same.
An object starts from rest and slides with negligible friction down an air track tipped at an angle θ from the horizontal. A student records values of the object's position along the track at various times. The value of θ can best be determined from which of the following?
The slope of a graph of position as a function of the square of time
A student sets an object attached to a spring into oscillatory motion and uses a motion detector to record the velocity of the object as a function of time. A portion of the recorded data is shown in the figure above. The acceleration of the object at time t = 0.7 s is most nearly equal to which of the following?
The slope of the tangent to a best-fit sinusoidal curve at 0.7 s
A spaceship is traveling from Earth to the Moon. Which of the following is true of the gravitational force on the ship due to the two objects when the ship is equidistant from Earth and the Moon?
There is a net force because the force exerted by Earth is greater than that exerted by the Moon.
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 < 2 fT
A small block slides without friction along a track toward a circular loop. The block has more than enough speed to remain firmly in contact with the track as it goes around the loop. The magnitude of the block's acceleration at the top of the loop is
greater than g
Two identical blocks slide along a ramp with negligible friction, as shown. The first block has an initial speed v0 up the ramp while the second has the same initial speed v0 down the ramp. The coordinate system shown defines down the ramp to be the positive x direction. While both blocks are sliding on the ramp, the center of mass velocity of the two-block system is
increasing in the +x direction Correct. The center of mass velocity of any system will accelerate in the direction of the net force on the system. In this case, the initial center of mass velocity is zero since the blocks are identical and are given equal and opposite velocities. The net force on the system is directed down the ramp (the +x-direction) and so the acceleration of the center of mass of the system will be in the +x-direction. Since the initial velocity of the center of mass is zero, the center of mass velocity will begin to increase down the ramp in the +x direction.
An artificial satellite orbits Earth at a speed of 7800 m/s and a height of 200 km above Earth's surface. The satellite experiences an acceleration due to gravity of
less than 9.8 m/s2 but greater than zero
Blocks A and B, of masses mA and mB, are at rest on a frictionless surface, as shown above, with block A fixed to the table. Block C of mass mC is suspended by a string that is tied to block B over an ideal pulley. Which of the following gives the magnitude of the force exerted by block A on block B ?
mCg
A ball of mass m is attached to a vertical rod by two massless strings. The rod is rotated about its axis so that both strings are taut, with tensions T1 and T2, respectively. The strings and rod form the right triangle shown in the figure above. The ball rotates in a horizontal circle of radius r with speed v. What is the tension T1 in the upper string?
mg/cos θ
An object of mass m is attached to a spring on a frictionless inclined plane that makes an angle θ with the horizontal, as shown above. The object is released from rest with the spring in its unstretched position. As the object moves on the plane, its displacement from the unstretched position is x. The object subsequently oscillates about an equilibrium position at a displacement x0 from the unstretched position of the spring. What is the spring constant of the spring?
mgsintheta/x0
A person of mass 60kg is initially standing at one end of a small raft that has a mass of 40kg. The raft is in the middle of a lake, and the drag force between the raft and the water is negligible. The person begins to walk to the right, as shown above, at a speed v relative to the water. As a result, the raft will
move to the left at a speed greater than v Correct. There is no net external force on the system, so the total momentum of the system with respect to the water must be zero. mpv p−mr vr=0. Solving for the speed of the raft yields vr=mp/mr vp . This indicates that the speed of the raft will be greater than the speed of the person, because the mass of the person is greater than the mass of the raft.
A ball of mass m is attached to a vertical rod by two massless strings. The rod is rotated about its axis so that both strings are taut, with tensions T1 and T2, respectively. The strings and rod form the right triangle shown in the figure above. The ball rotates in a horizontal circle of radius r with speed v. What is the magnitude of the net force on the ball?
mv^2 / r
A student wants to determine the coefficient of static friction μ between a block of wood and an adjustable inclined plane. Of the following, the minimum additional equipment the student needs to determine a value for μ is
protractor only
Two satellites are in circular orbits around Earth. Satellite A has speed vA. Satellite B has an orbital radius nine times that of satellite A. What is the speed of satellite B?
vA/3
A cart is traveling in the positive direction with speed v0 on a horizontal, frictionless track when it reaches position x=0. The graph above shows the net horizontal force exerted on the cart as a function of position between x=0 and x=1m. The cart's speed at x=1m is vf.
vf > vo Correct. The area under the curve represents the work done on the car. The total area from x=0 to x=1 m is positive, resulting in a positive change in kinetic energy, so vf must be greater than v0.
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 correctly ranks the displacement ∆x for the three segments of the object's motion?
∆x3 > ∆x2 > ∆x1 > 0
