AP Physics 1 Final
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.
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
An object is sliding to the right along a straight line on a horizontal surface. The graph shows the object's velocity as a function of time. What is the object's displacement during the time depicted in the graph?
0 m
Assume the elevator is moving at constant speed, and consider the bottom box in the stack that has two boxes of mass 2M. Let Ffloor be the force exerted by the floor on the box, Fg be the force exerted by gravity on the box, and Fbox be the force exerted by the top box on the bottom box. Which of the following best represents the forces exerted on the bottom box?
1 pointing up and 2 pointing down
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/s2
At time t=0, a moving cart on a horizontal track is at position 0.5m. Using a motion detector, students generate a graph of the cart's velocity as a function of time, as shown above. At t=2.5s, the cart's position is most nearly
1.75m
A 50 kg athlete running at speed v grabs a light rope that hangs from a 10-meter-high platform and swings to a maximum of 1.8 m above the ground. Later, a 100 kg athlete, running at the same speed, grabs a similar rope hanging from a 5-meter-high platform. What is the maximum height to which the 100 kg athlete swings?
1.8 m
An object has a weight W when it is on the surface of a planet of radius R. What will be the gravitational force on the object after it has been moved to a distance of 4R from the center of the planet?
1/16W
Two students want to determine the speed at which a ball is released when thrown vertically upward into the air. One student throws the ball into the air while the other student measures the total time that the ball is in the air. The students use a meterstick to measure the release height of the ball. Which of the following equations should the students use to determine the speed at which the ball was released?
1/2ayt^2 from the moment in time in which the ball was released to the moment in time in which the ball hits the ground.
A rock of mass m is thrown horizontally off a building from a height h, as shown above. The speed of the rock as it leaves the thrower's hand at the edge of the building is vo What is the kinetic energy of the rock just before it hits the ground?
12 mv2+mgh
A ball is attached to one end of a string such that the ball travels in a vertical circular path near Earth's surface. The force diagram of the ball at its lowest point in the circular path is shown above. What is the net centripetal force exerted on the ball?
15 N
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
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 vectors, normal force diagonal to the ramp
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?
4 vectors, F sub c pointing to right
An object is thrown with a horizontal velocity of 20 m/s from a cliff that is 125 m above level ground. If air resistance is negligible, the time that it takes the object to fall to the ground from the cliff is most nearly
5 s
A student wants to investigate the motion of a ball by conducting two different experiments, as shown in Figure 1 and Figure 2 above. In Experiment 1, the student releases a ball from rest and uses a slow-motion camera to film the ball as it falls to the ground. Using video analysis, the student is able to plot the ball's horizontal position xx and vertical position y as a function of time t. In Experiment 2, the student horizontally rolls the same ball off a table, and uses video analysis to plot the ball's horizontal position xx and vertical position y as a function of time t starting from the instant the ball leaves the table. The graphs from each experiment are shown above along with each graph's best-fit curve line.
5.4m/s
The graph above represents position x versus time t for an object being acted on by a constant force. The average speed during the interval between 1 s and 2 s is most nearly
6 m/s
A ball is dropped from rest and falls to the floor. The initial gravitational potential energy of the ball-Earth-floor system is 10 J. The ball then bounces back up to a height where the gravitational potential energy is 7 J. What was the mechanical energy of the ball-Earth-floor system the instant the ball left the floor?
7 J
Object A is released from rest at height h. At the same instant, object B is thrown downward from the same location. Which of the following graphs of speed of v as a function of time t is correct for the two objects?
A Diagonal from (0,0) B above A on y-axis, perpendicular to A
In which of the following situations is the kinetic energy of the object decreasing?
A baseball is heading upward after being thrown at an angle.
The diagram above shows the forces exerted on an object. Which of the following dot diagrams best represents the position of the object at equal time intervals?
Dots getting further apart in a horizontal line
A rocket is continuously firing its engines as it accelerates away from Earth. For the first kilometer of its ascent, the mass of fuel ejected is small compared to the mass of the rocket. For this distance, which of the following indicates the changes, if any, in the kinetic energy of the rocket, the gravitational potential energy of the Earth-rocket system, and the mechanical energy of the Earth-rocket system?
Everything Increasing
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.
Blocks A and B, of masses mm and 2m2m, respectively, are connected by a light string and pulled across a surface of negligible friction with a constant force F1, as shown above. The acceleration of the blocks is aa. The force of the string pulling block B forward has magnitude F2. Which of the following claims correctly describes the relationship between the magnitude of the forces acting on the blocks?
F1 is greater than F2.
Object X and object Y are at rest on a horizontal surface. Object X is in contact with object Y. The force diagrams for both objects are shown above. Which two forces make up an action-reaction pair?
F3 and F6, because both forces are exerted on different objects, have the same magnitude, and are in opposite directions.
A student makes the necessary measurements to create the graph shown, which represents the vertical component of the velocity as a function of time for the dart and for the target from t=0t=0 until the instant the dart hits the target. At t=0t=0, the target is a vertical distance h above the dart. The curves for the dart and the target each have the same area between them and the horizontal axis. Both curves also have the same slope. Which of the following is the best method to determine the distance h from the graph?
Find twice the area under the curve for the dart's data.
The student collects the data necessary to graph the object's kinetic energy as a function of time, as shown. Which of the following graphs represents the sum of the kinetic energy KK and gravitational potential energy UgUg of the object-Earth system as a function of time?
Horizontal line from 2500
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.
An object attached to one end of a string moves in a circle at constant speed. Which of the following is correct?
The object is accelerating as it moves.
A lion is running at constant speed toward a gazelle that is standing still, as shown in the top figure above. After several seconds, the gazelle notices the lion and accelerates directly toward him, hoping to pass the lion and force him to reverse direction. As the gazelle accelerates toward and past the lion, the lion changes direction and accelerates in pursuit of the gazelle. The lion and the gazelle eventually each reach constant but different speeds. Which of the following sets of graphs shows a reasonable representation of the velocities of the lion and the gazelle as functions of time?
Lion below and above negative, gazelle positive with horizantal line from origin
A ball is thrown straight up in the air. When the ball reaches its highest point, which of the following is true?
None of the above
A cart of mass mm is moving with speed vv on a smooth track when it encounters a vertical loop of radius RR, as shown above. The cart moves along the inside of the entire loop without leaving the track. All frictional forces are negligible.
Normal to the right gravity pointed down
A steel ball supported by a stick rotates in a circle of radius r, as shown above. The direction of the net force acting on the ball when it is in the position shown is indicated by which of the following?
Pointed towards the center
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 ?
Pointing down
The graphs above represent the position x, velocity v, and acceleration a as a function of time t for a marble moving in one dimension. Which of the following could describe the motion of the marble?
Rolling up a ramp and then rolling back down
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 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.
Two blocks are connected by a rope, as shown above. The masses of the blocks are 5 kg5 kg for the upper block and 10 kg10 kg for the lower block. An upward applied force of magnitude FF acts on the upper block.
The block continues to move upward but begins to accelerate downward.
A student wants to approximate the amount of work that the force due to gravity does on the student as the student walks up a set of stairs. Which of the following measurements must the student collect in order to approximate the amount of work done by Earth on the student? Select two answers.
The final vertical height above the initial vertical position. The mass of the student.
An astronaut in the space station appears weightless because the astronaut seems to float. Which of the following claims is true about the force exerted on the astronaut by Earth?
The force exerted on the astronaut by Earth is equal to the force exerted on Earth by the astronaut.
A planet travels in an elliptical path around a star, as shown in the figure. As the planet gets closer to the star, the gravitational force that the star exerts on the planet increases. Which statement of reasoning best supports and correctly identifies what happens to the magnitude of the force that the planet exerts on the star as the planet gets closer to the star?
The force increases because it is part of a Newton's third law pair of forces with the force that the star exerts on the planet.
An astronaut stands on the surface of an asteroid. The astronaut then jumps such that the astronaut is no longer in contact with the surface. The astronaut falls back down to the surface after a short time interval. Which of the following forces CANNOT be neglected when analyzing the motion of the astronaut?
The gravitational force between the astronaut and the asteroid
A ball is dropped onto the floor and bounces upward. Which of the following claims are correct about the force that the ball exerts on the floor compared to the force that the floor exerts on the ball when the ball and the floor are in contact?
The magnitude of the forces exerted by both objects is the same because the ball and the floor cannot exert forces of different magnitudes on each other.
A conveyor belt ramp of length 7m7m is inclined at 20°20° with respect to the horizontal and is used to move objects from one location to another location. When an object is placed on the conveyor belt, the object travels up the incline with a constant speed of 1.5 ms1.5 ms . A motor is used to keep the conveyor belt moving. The mass of the objects that are placed on the conveyor belt are varied.
The mechanical energy of the object is constant because the kinetic energy of the object is constant.
A cart of mass mm is moving with speed v on a smooth track when it encounters a vertical loop of radius RR, as shown above. The cart moves along the inside of the entire loop without leaving the track. All frictional forces are negligible.
The net force exerted on the cart must be equal to or greater than the weight of the cart.
A crate is on a horizontal frictionless surface. A force of magnitude F is exerted on the crate at an angle θ to the horizontal, as shown in the figure above, causing the crate to slide to the right. The surface exerts a normal force of magnitude FN on the crate. As the crate slides a distance d, it gains an amount of kinetic energy ∆K. While F is kept constant, the angle θ is now doubled but is still less than 90o. Assume the crate remains in contact with the surface.
The new gain is less than ∆K
A ball is tossed straight up and later returns to the point from which it was launched. If the ball is subject to air resistance as well as gravity, which of the following statements is correct?
The speed at which the ball returns to the point of launch is less than its speed when it was initially launched.
A block of mass MM is released from rest at point 1, as shown in the figure. The block slides without frictional forces along the circular arc but encounters frictional forces as soon as it reaches the horizontal portion of the track at point 2. The block travels a distance DD along the horizontal track before coming to rest at point 3. Consider the block-Earth system. In terms of the mechanical energy of the system, which of the following claims is correct, and why?
The system is open, because there is a net force exerted on the block.
An amusement park ride has two identical carriages that revolve around the center of the ride's axle, as shown in the figure. Both carts travel at a constant tangential speed at all points along the circular path. At what position is the total mechanical energy of the cart-cart-Earth system at its maximum value?
The total energy of the Earth-Ferris wheel ride is constant.
A person holds a book at rest a few feet above a table. The person then lowers the book at a slow constant speed and places it on the table. Which of the following accurately describes the change in the total mechanical energy of the Earth-book system?
The total mechanical energy decreases, because the person does negative work on the book by exerting a force on the book in the direction opposite to its displacement.
An inclined track is secured to a table. The height of the highest point of the track above the tabletop is h1h1. The height from the tabletop to the floor is h2h2. A block of mass MM is released from rest and slides down the track such that all frictional forces are considered to be negligible. The block leaves the track horizontally and strikes the ground at a distance DD from the edge of the track as shown. Which of the following statements is correct about the scenario? Select two answers.
The total mechanical energy of the system containing only the block increases from the moment of release to the moment it strikes the ground. The total mechanical energy of the block-Earth system remains constant.
A comet passes by a planet with a speed vo such that the comet travels in a straight line at the instant shown in the figure. The comet's tangential acceleration, centripetal acceleration, and force due to gravity from the planet at this location are provided in the table. Astronomers observe that the comet continues to travel in a nearly straight line, even though calculations show that the gravitational force exerted by the planet should cause the comet to move in a circular orbit. Why does the comet not travel in a circular path around the planet after the instant shown in the figure?
There must be another object such that the gravitational forces exerted on the comet are balanced at this location.
An object slides across a horizontal surface such that it slows down due to the force of friction that is exerted on the object. The object and the direction of its displacement are shown in the figure. Which of the following free-body diagrams could represent the forces that are exerted on the object?
Tiny Friction, even normal and gravity
One end of a string is attached to a vertical pole with the other end of the string attached to a ball that swings in a horizontal circular path, as shown. Which of the following free body diagrams represents the forces exerted on the ball?
Up and diagonal to the left and one straight down
A person throws a marble straight up into the air, releasing it a short height above the ground and catching it at that same height. If air resistance is negligible, which of the following graphs of position y versus time t is correct for the motion of the marble as it goes up and then comes down?
Upside down parabola
A student drops a rock from the top of a cliff such that the rock falls downward toward Earth's surface in the absence of air resistance. The downward direction is considered to be the positive direction. The graph shows the rock's velocity as a function of time. Which of the following methods should be used to determine the total distance traveled by the rock after 4s4s ?
Use the area under the curve, as it states that the rock traveled 80 meters in total.
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?
case 2 then case 1
A rock of mass m is thrown horizontally off a building from a height h, as shown above. The speed of the rock as it leaves the thrower's hand at the edge of the building is vo How much time does it take the rock to travel from the edge of the building to the ground?
square root 2h/g
An object is thrown with an initial speed v near the surface of Earth. Assume that air resistance is negligible and the gravitational field is constant. If the object is thrown vertically upward, the direction and magnitude of its acceleration while it is in the air is
downward and constant
A ball of mass M swings in a horizontal circle at the end of a string of radius R at a constant tangential speed v0. A student gradually pulls the string inward such that the radius of the circle decreases while keeping the tangential speed v0 of the ball constant, as shown above. Which of the following graphs best represents the acceleration aa of the ball as a function of time t?
exponential growth
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?
straight up and diagonal from (0,0)
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
While traveling in its elliptical orbit around the Sun, Mars gains speed during the part of the orbit where it is getting closer to the Sun. Which of the following can be used to explain this gain in speed?
As Mars gets closer to the Sun, the Mars-Sun system loses potential energy and Mars gains kinetic energy.
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 20 s and 30 s
Figure 1 shows a displacement-versus-time graph for the dart. Figure 2 shows a displacement-versus-time graph for the target. For both graphs, the component of the displacement is not indicated. Which displacement component, horizontal or vertical, is represented by the graph for each object?
Both Vertical
The motion of a particle along a straight line is represented by the position versus time graph above. At which of the labeled points on the graph is the magnitude of the acceleration of the particle greatest?
C
Which of the following graphs could represent the vertical component of the velocity as a function of time for the dart and the target immediately after the dart is launched and the target begins to fall?
Dart positive y axis with negative slope Target negative y axis with negative slope from origin
A crate is on a horizontal frictionless surface. A force of magnitude F is exerted on the crate at an angle θ to the horizontal, as shown in the figure above, causing the crate to slide to the right. The surface exerts a normal force of magnitude FN on the crate. As the crate slides a distance d, it gains an amount of kinetic energy ∆K. While F is kept constant, the angle θ is now doubled but is still less than 90o. Assume the crate remains in contact with the surface.
The new normal force is less than FN.
A cart is constrained to move along a straight line. A varying net force along the direction of motion is exerted on the cart. The cart's velocity v as a function of time t is shown in the graph above. The five labeled points divide the graph into four sections. Which of the following correctly ranks the magnitude of the average acceleration of the cart during the four sections of the graph?
aCD > aAB > aDE > aBC
