Physics final
A car goes from rest to 30 m/s in 12 s with constant acceleration. How long does it take the car to go from rest to 15 m/s with the same acceleration?
(C) 6.0 s
Two objects, X and Y, accelerate from rest with the same constant acceleration. Object X accelerates for twice the time as object Y. Which of the following is true of these objects at the end of their respective periods of acceleration?
(E) Object X has traveled four times as far as object Y.
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?
(C) 7 J
Two blocks of masses m and M are suspended as shown 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
(E) M(g-a)
A ball is thrown straight up in the air. When the ball reaches its highest point, which of the following is true?
(E) None of the above
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?
(A)
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?
(A) (the constant and evenly spaced dots)
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. Rock 1, of mass m, reaches a maximum height hmax after being launched. During the time between the instant rock 1 is launched from height h0 and the instant it returns to height h0, the work done on the rock by the gravitational force is
(A) 0
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.
(A) 6 N and (B) 10 N
For which segment does the cart move the greatest distance?
(A) AB
At time t = 0, Car X traveling with speed v₀ passes Car Y. which is just starting to move. Both cars then travel on two parallel lanes of the same straight road. The graphs of speed v versus time t for both cars are shown above .Which of the following is true at time t=20 seconds?
(A) Car Y is behind Car X
The Atwood's machine shown consists of two blocks of mass m1, and m2 that are connected by a light string that passes over a pulley of negligible friction and negligible mass. The block of mass m1 is a distance h1, above the ground, and the block of mass m2, is a distance h2, above the ground. m2 is larger than m1. The two-block system is released from rest. Which of the following claims correctly describes the outcome after the blocks are released from rest but before the block of my reaches the ground? Select two answers.
(A) For the system consisting of the two blocks, the change in the kinetic energy of the system is equal to the work done by gravity on the system. (D) For the system consisting of the two blocks, the pulley, and Earth, the change in the total mechanical energy of the system is zero.
A stick is used to hit a ball at an angle above the horizontal, as shown in Figure 1. Figure 2 shows the free body diagram of the ball. Figure 3 shows the free body diagram of the stick. Which of the following pairs of forces represents an action-reaction pair and the object or objects involved in the action-reaction pair?
(A) Fstick and Fball
A whiffle ball is tossed straight up, reaches a highest point, and falls back down. Air resistance is not negligible. Which of the following statements are true?
(A) I. The ball's speed is zero at the highest point, only.
A motion sensor is used to create the graph of a student's horizontal velocity as a function of time as the student moves toward and away from the sensor, as shown above. The positive direction is defined as the direction away from the sensor. Which of the following describes the student's final position x in relation to the starting position x₀ and the student's average horizontal acceleration ax between 0.0 s and 3.0s?
(A) Position Xf is farther away from the sensor than x0 and ax is negative
Two frictionless lab carts start from rest and are pushed along a level surface by a constant force. Students measure the magnitude and duration of the force on each cart, as shown in the partially completed data table above, and calculate final kinetic energy and momentum. Which cart has a greater kinetic energy at the end of the push?
(A) The 1 kg cart
An object attached to one end of a string moves in a circle at constant speed. Which of the following is correct?
(A) The object is accelerating as it moves.
A block of mass M 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 D 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?
(A) The system is open, because there is a net force exerted on the block
The stack of boxes shown in 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. How does the magnitude of the force exerted by the top box on the bottom box compare with the magnitude of the force exerted by the bottom box on the top box?
(A) The two magnitudes are always equal in each of the stacks.
One end of a string is attached to the ceiling with the other end attached to a toy. The toy can be set into motion such that it travels in a horizontal circular path at a constant tangential speed, as shown above. The toy experiences a component of the tension force toward the center of the circular path that serves as the centripetal force exerted on the toy. Which of the following measurements could a student use to determine the net centripetal force exerted on the toy? Select two answers.
(A) Use a scale to determine the mass of the toy. Use a protractor to determine the angle θ between a vertical line and the angle that the string makes with the vertical line. (B) Use a stopwatch to determine the time for the toy to complete one revolution. Use a meterstick to measure the radius of the toy's circular path, R. Use a scale to determine the mass of the toy.
The free fall trajectory of an object thrown horizontally from the top of a building is shown as the dashed line in the figure. Which sets of arrows best correspond to the directions of the velocity and of the acceleration for the object at the point labeled P on the trajectory?
(A) Velocity: Diagonally bottom right, Acceleration: straight down
A diver initially moving horizontally with speed v dives dives off the edge of a vertical cliff and lands in the water a distance d from the base of the cliff. How far from the base of the cliff would the diver have landed if the diver initially had been moving horizontally with speed 2v?
(C) 2d
The velocity of a projectile at launch has a horizontal component Vh and a vertical component Vv. Air resistance is negligible. When the projectile is at the highest point of its trajectory, identify the vertical and the horizontal components of its velocity and the vertical component of its acceleration?
(A) Vertical Velocity: 0, Horizontal Velocity: Vh, Vertical Acceleration: g
Would you need to linearize this graph?
(A) Yes
The displacement x of an object moving along the x-axis is shown above as a function of time t. The acceleration of this object must be
(A) Zero
A block is released from rest and slides down a frictionless ramp inclined at 30⁰ from the horizontal. When the block reaches the bottom the block-Earth system has mechanical energy E0. The experiment is repeated, but now horizontal and vertical forces of magnitude F are exerted on the block while it slides, as shown above. When the block reaches the bottom, the mechanical energy of the block-Earth system
(A) is greater than E 0
Which of the following correctly ranks the displacement Δx for the three segments of the object's motion?
(A) Δx₃> Δx₂ > Δx₁ > 0
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?
(B)
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 graphs best represents the kinetic energy K of the object as a function of time?
(B) (increases in curves until it becomes constant)
An object is released from rest near a planet's surface. A graph of the acceleration as a function of time for the object is shown for the 4 s after the object is released. The positive direction is considered to be upward What is the displacement of the object after 2 s?
(B) -10m
What is the displacement travelled according to the graph below:
(B) -3m
During an experiment, an object is placed on a disk that rotates about an axle through its center, as shown in Figure 1. The disk is a distance R =0.10 m from the center and rotates with a constant tangential speed of 0.60 m/s. A free body diagram of the forces exerted on the block is shown in Figure 2 with an unknown force of friction. What is the force of friction exerted on the object?
(B) 0.72 N
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
(B) 1.0 m/s²
A 0.5kg object is in free fall as it falls downward near the surface of a planet. A graph of the object's velocity as a function of time is shown. What is the force due to gravity exerted on the object by the planet?
(B) 1.25 N
A ball is thrown with an initial speed of 20 m/s at an angle of 60° to the ground. If air resistance negligible, what is the ball's speed at the instant it reaches its maximum height from the ground?
(B) 10 m/s
A 4 kg block is pushed up an incline that makes a 30⁰ angle with the horizontal, as shown in the figure. Once the block is pushed a distance of d=5.0 m up the incline, the block remains at rest. What is the approximate change in the gravitational potential energy of the block-Earth system when the block is held at rest compared to its original location at the bottom of the incline?
(B) 100 J
A force F is exerted on 5 kg block to move it across a rough surface, as shown above. Magnitude of force is initially 5 N, and the block moves at a constant velocity. While the block is moving, the force is instantaneously increased to 12 N. How much does kinetic energy lose or gain as it moves 2 m?
(B) 14 J
A student is observing an object of unknown mass that is oscillating horizontally at the end of an ideal spring. The student measures the object's period of oscillation with a stopwatch. Using a number of measurements, the student determines the following: Spring Constant: 85 N/m Mass of object: 0.50 kg Amplitude of oscillation: 0.30 m Maximum speed of object: 3.9 m/s The total energy of the obejct-spring system is most nearly
(B) 3.8 J
A horizontal, uniform board of weight 125 N and length 4 m is supported by vertical chain at each end. A person weighing 500 N is sitting on the board. The tension in the right chain is 250 N. What is the tension in the left chain?
(B) 375 N
A 2kg object is a distance of 10,000,000 m away from the center of Earth, which has a mass of nearly 6x10²⁴ kg. What is the approximate gravitational field strength of Earth's gravitational field at the location of the 10kg object?
(B) 4 N/kg
A car travels 30 miles at an average speed of 60 miles per hour and then 30 miles at an average speed of 30 miles per hour. The average speed of the car over the 60 miles
(B) 40 mph
A block is projected up a frictionless plane with an initial speed v₀. 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?
(B) 5 m/s² down the incline
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, what is the frictional force exerted on the block?
(B) 7 N
The graph above shows the potential energy U of a system as one object moves along the x-axis and the rest of the system does not move. Six evenly-spaced points along the x-axis are labeled. At point H, the object is moving in the positive x-direction and the mechanical energy of the system is 5.0 J. As the object moves, no energy enters or leaves the system. What is the kinetic energy of the object at point K?
(C) 3 J
A student performs an experiment in which the horizontal position of a toy car is recorded on ticker tape from a device that places dots on the tape in equal time intervals. The series of dots in the figure represents the motion of an object moving from the negative direction to the positive direction along the horizontal direction. The time interval between each recorded dot is 1s. Which of the following experiments could the student have conducted to create the data shown on the ticker tape?
(B) A toy car that initially increases its speed, travels at a constant speed, and then decreases its speed.
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?
(B) Between 20 s and 30 s
A student must determine the inertial mass of a block that is pulled across a horizontal surface using a force probe an an accelerometer. The student's data are represented in the graph above. What must the student do to determine the inertial mass of the block?
(B) Calculate the slope.
An object is moving to the right with speed Vi when a force of magnitude F is exerted on it. In which situation in the link is the object's direction of motion changing and kinetic energy decreasing at the instant shown?
(B) Force is applied to the top left, while velocity still points right
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, and 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?
(B) The acceleration is directed downward with magnitude equal to g because the system is a projectile.
A planet has two moons, Moon A (closer) and Moon B (farther), that orbit at different distances from the planet's center, as shown. Astronomers collect data regarding the planet, the two moons, and their obits. The astronomers are able to estimate the planet's radius and mass. The masses of the two moons are determined to be 2M for Moon A and M for Moon B. It is observed that the distance between Moon B and the planet is two times that of the distance between Moon A and the planet. How does force exerted from the planet on Moon A compare to the force exerted from the planet on Moon B?
(B) The gravitational force exerted from the planet on Moon A is eight times larger than the gravitational force exerted from the planet on Moon B.
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. During some part of the motion, the work done on the cart is negative. What feature of the motion indicates this?
(B) The speed is decreasing.
A student predicts that a block sliding down a ramp inclined at 45 degrees should have an acceleration of approximately 7 m/s². The block is released from rest, and the student measures the distance the block travels and the time it takes to travel that distance. The student determines that the block's acceleration is only 5.5 m/s². Which of the following is the most likely reason for the difference between the predicted and calculated accelerations?
(B) The student's model used to make the prediction did not account for all of the forces that are exerted on the block.
A student swings a ball at the end of a string of length R in a vertical circle as shown. The ball moves with the minimum speed necessary to complete a circular path at point 1. Consider the system of the ball. In terms of the mechanical energy of the system, which of the following claims is correct, and why?
(B) The system is open, because a net force is exerted on the ball as it travels in a circle.
The diagram shows the forces exerted on a block that starts from rest and speeds up as it moves down a rough incline near Earth's surface. Which of the following statements are true? Select two answers
(B) The total mechanical energy of the block-Earth system decreases as the block slides down the incline. (C) The momentum of the block increases as the block slides down the incline.
A train is traveling east with constant speed Vt. Two identical spheres are rolling on the floor of one rain car. In the frame of reference of the train, the spheres are moving directly towards each other at one instant with the same speed vp parallel tot he train's motion, as shown in the figure above. What is the velocity of the center of mass of the spheres in the frame of reference of the train and in the frame of reference of a person standing at rest alongside the train?
(B) Train Person Zero Vt east
A person driving a car suddenly applies the brakes. The car takes 4 s to come to rest while traveling 20 m at constant acceleration. Can the speed of the car immediately before the brakes were applied be determined without first determining the car's acceleration?
(B) Yes, by determining the average speed while braking and doubling it.
A force F0 is applied continuously to a box initially at rest on a horizontal surface. The box slides with negligible friction for equal distances d1 and d2, as shown. How does the kinetic energy gained by the block over distance interval d2, ΔK2, compare to the kinetic energy gained over distance interval d1, ΔK1, and why?
(B) ΔK2=ΔK1, because applied force does the same work on the block over intervals d1 and d2.
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
(C) 20 m
A moon of mass 1 x 10²⁰ kg is in circular orbit around a planet. The planet exerts a gravitational force of 2 x 10²¹ N on the moon. The centripetal acceleration of the moon is most nearly
(C) 20 m/s²
An object is moving in the positive x-direction while a net force directed along the x-axis is exerted on the object. The figure shows the force as a function of position. What is the net work done on the object over the distance shown?
(C) 2F0d
An object is released from rest on a planet that has no atmosphere. The object falls freely for 3.0 meters in the first second. What is the magnitude of the acceleration due to gravity on the planet?
(C) 6.0 m/s²
Three stones of different mass (1 m, 2m & 3m) are thrown vertically upward with different velocities (l v, 2v & 3v respectively). The diagram indicates the mass and velocity of each stone. Rank from high to low the maximum height of each stone. Assume air resistance is negligible.
(C) III, II, and I (basically from greatest to least)
The graph above shows the potential energy U of a system as one object moves along the x-axis and the rest of the system does not move. Six evenly-spaced points along the x-axis are labeled. At point H, the object is moving in the positive x-direction and the mechanical energy of the system is 5.0 J. As the object moves, no energy enters or leaves the system. In which segment does the net force exerted on the object have the greatest magnitude?
(C) J L
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?
(C) Only the mass of Block A and the distance block A falls to reach the floor
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?
(C) Rolling up a ramp then rolling back down
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. The system is moving and accelerating upward. A pair of scissors cuts the rope. Which of the following describes the motion of the 10 kg block immediately after the rope has been cut?
(C) The block continues to move upward but begins to accelerate downward.
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?
(C) The only one where both Fg and Fbox point downward.
An inclined track is secured to a table. The height of the highest point of the track above the tabletop is h1. The height from the tabletop to the floor is h2. A block of mass M 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 D from the edge of the track as shown. Which of the following statements are correct about the scenario? Select two answers
(C) The total mechanical energy of the system containing only the block increases from the moment of release to the moment it strikes the ground. (D) The total mechanical energy of the block-Earth system remains constant.
The box experiences a varying net force that changes its velocity. The graph shows the velocity of the box as a function of time. Which of the following correctly describes the net work, Wnet, done on the box for the given intervals of time?
(C) Wnet=0, Wnet=0, and Wnet < 0
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 v0. How much time does it take the rock to travel from the edge of the building to the ground?
(C) √2h/g
A projectile is fired with initial velocity vo at an angle T0 with the horizontal and follows the trajectory shown above. Which of the following pairs of graphs best represents the vertical components of the velocity and acceleration, v and a, respectively, of the projectile as functions of time t?
(D) (decreasing velocity and constant acceleration)
A large beach ball is dropped from the ceiling of a school gymnasium to the floor about 10 meters below. Which of the following graphs would best represent its velocity as a function of time? (do not neglect air resistance)
(D) (its the only graph that curves upward)
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
(D) 2.0m/s²
A 2kg object is initially at rest at time t = 0 s. It then slides across a rough, horizontal surface under the influence of only the four forces shown in the table above. What is the speed of the object at time t = 3 s?
(D) 36 m/s
A block on a horizontal surface is placed in contact with a light spring with spring constant k, as shown in Figure 1. When the block is moved to the left so that the spring is compressed a distance d from its equilibrium length, the potential energy stored in the spring-block system is Em. When a second block of mass 2m is placed on the same surface and the spring is compressed a distance 2d, as shown in Figure 2, how much potential energy is stored in the spring compared to the original potential energy Em? All frictional forces are considered to be negligible.
(D) 4K₁
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
(D) 6 m/s
The diagram below shows three cannons firing shells with different masses at different angles of elevation. The horizontal component of the shell's velocity is the same in all four cases. In which case will the shell have the greatest range if air resistant is neglected?
(D) Both cannons B and C have the greatest range
A block of mass M is released from rest and slides down an incline, as shown in the figure. The length D of the incline is 0.8 m and the angle of the incline, θ, is 37⁰. A graph of the speed v as a function of time t of the block as it descends the incline is shown. How could a student use the graph and the information provided to determine whether the block-Earth system is an open system or a closed system?
(D) Determine final kinetic energy as described above and compare it with the initial gravitational potential energy of the block-Earth system as described above.
A student is asked to determine the work done on a block of wood when the block is pulled horizontally using an attached string. The student is supplied with a spring scale, a stopwatch, and a meterstick. Which of the following graphical analysis techniques will allow the student to determine the work done on the block by the string?
(D) Graphing the force as a function of distance and calculating area under the curve
A block slides to the right on a rough horizontal surface. The forces exerted on the block are shown above. Which of the following statements about the frictional force Ff exerted on the block is true?
(D) It is the sum of all the microscopic contact forces between the bottom of the block and the surface.
The figure above shows the position of a moon that orbits a planet in an elliptical path. Two specific locations of the moon, position A and position B, are labeled. As the moon orbits the planet from position A to position B, is the magnitude of the planet's force due to gravity exerted on the moon constant? Why or why not?
(D) No, because the moon's distance from the planet is always changing.
A student must design an experiment to determine the relationship between the mass of an object and the resulting acceleration when the object is under the influence of a net force. Which of the following experiments should the student conduct in order to determine the relationship between all three quantities?
(D) Slide an object of known mass across a rough surface, using a constant applied force that can be measured by a force sensor. Place a motion detector behind the object so that its speed can be measured as it slides across the surface. Repeat the experiment for different applied forces.
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?
(D) Tcos(θ)-μ(Mg-Tsin(θ))
A student uses both hands to push a door such that it moves and swings open after the force has been applied. The student then makes the following claim: "I can use both of my hands to apply a constant force on my body so that my body falls backward." Which of the following statements correctly justifies the student's claim?
(D) The claim is not correct because the student's body will exert a force of equal magnitude back on the student's hands as a result of Newton's third law of Motion.
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?
(D) The gravitational force between the astronaut and asteroid
A student conducts an experiment in which a 0.5 kg ball is spun in a vertical circle from a string of length 1 m, as shown in the figure. The student uses the following equation to predict the force of tension exerted on the ball whenever it reaches the lowest point of its circular path at a known tangential speed for various trials. FTension=mv2r. When the experiment is conducted, the student uses a force probe to measure the actual force of tension exerted on the ball. Why is the predicted force of tension different than the actual force of tension?
(D) The student did not account for the downward force due to gravity at the ball's lowest point along its circular path, so the predicted force of tension is the net centripetal force exerted on the ball.
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?
(D) 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?
(D) 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 of its displacement.
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?
(D) There must be another object such that the gravitational forces exerted on the comet are balanced at this location.
Which of the following correctly ranks the magnitude of the average acceleration of the cart during the four sections of the graph?
(D) aCD > aAB > aDE > aBC
A block of mass m₁ collides with a block of mass m₂ such that block of mass m₁ becomes at rest while block of mass m₂ slides across a surface of negligible as it travels with a constant speed toward the frictional surface, as shown above. The coefficient of kinetic friction between block of mass m₂ and the frictional surface is μk. What is the rate of change of the speed of the center of mass of the two-block system after the block of mass m₂ enters the frictional surface?
(D) μkm₂g/(m₁+m₂)
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?
(E) 1/16 W
Balls 1 and 2 are each thrown horizontally from the same height above level ground, but ball 2 has a greater initial velocity after leaving the thrower's hand. If air resistance is negligible, how do the accelerations of the balls and the times it takes them to hit the ground compare?
(E) Acceleration a Time to Hit Ground Equal Equal
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
(E) F/4
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 v0. How much time does it take the rock to travel from the edge of the building to the ground?
(E) √2h/g
What is the distance travelled according the graph below (its a distance versus time graph):
(F) 11 m
The energy bar charts shown in the figure indicate the gravitational potential energy U and total Kinetic energy K for a system at two different times, t1 and a later time t2. The tables describe four different situations. For which of the situations could the energy bar charts accurately depict U and K at the two times? Select two answers.
Solution B and Solution D
