physics

Block X of mass m0 is at rest at the top of a ramp, and the block's center of mass is at a height H1 above the ground. Block X is then released from rest, and it slides down the ramp and collides with block Y of mass m0, which is initially at rest and has its center of mass at a height h above the ground. At the moment before the collision, block X has a speed of v0. After the collision, block Y travels such that it lands at point P. Consider the block X-block Y system from the moment in time that block X is released from rest to the moment immediately after block X collides with block Y. Which of the following claims best describes the system?

Because the total momentum of the system does not remain constant, the system is open.

Consider the block X-block Y system from the moment in time that block X is released from rest to the moment immediately after block X collides with block Y. Which of the following claims best describes the system?

Because the total momentum of the system does not remain constant, the system is open.

An object of mass 2 kg collides with an object of mass 1 kg that is at rest, as shown in the figure. A graph of the force as a function of time that the 1 kg object exerts on the 2 kg object is shown. After the collision, the 2 kg object has a speed of 2 m/s, and the 1 kg object has a speed of 8 m/s. A student must determine the initial speed v0 of the 2 kg object. Which of the following options shows the correct substitutions into the equatio

(2kg)(2 m/s - v0 ) = 1/2(8000N)(0.00125s), because the average force exerted on the 2 kg object must be considered.

A dart of mass md is launched straight upward toward a block of mass mb that hangs at rest from a string, as shown in Figure 1. Immediately before the dart collides with the block, the dart has a speed v0. The dart then collides with and sticks to the block, and the dart-block system travels upward to a height H before the system comes to rest, as shown in Figure 2. What is the change in momentum of the dart-block system immediately before the collision to the instant when the system comes to rest?

-mdv0

A car is moving along a straight horizontal road at a speed of 18.7 m/s. The brakes are applied and a constant force of 5,419 N decelerates the car to a stop in 8.3 s. What is the mass of the car in kg?

2,405.22

A 79.1 kg ice hockey goalie, originally at rest, catches a 0.188 kg hockey puck slapped at him at a velocity of 49.6 m/s. Suppose the goalie and the ice puck have an elastic collision and the puck is reflected back in the direction from which it came. What would their final velocity of the goalie be in this case if the final velocity of the puck is known to be -3.35 m/s?

0.126

A block of mass m slides along a frictionless surface with kinetic energy Ki. It collides with a block of mass 3m that is initially at rest, and the two blocks stick together and slide with total kinetic energy Kf. What is the ratio Kf : Ki?

1 : 4

Calculate the kinetic energy of a 6.4 kg block moving a speed of 24.2 m/s.

1,874.05

A rubber ball with mass 0.20 kg is dropped vertically from a height of 1.5 m above a floor. The ball bounces off of the floor, and during the bounce 0.60 J of energy is dissipated. What is the maximum height of the ball after the bounce?

1.2m

A ball of mass m and momentum p has kinetic energy equal to which of the following?

1/2 (v^2)/m

Calculate the momentum of a 1,770 kg elephant charging a hunter at a speed of 6.31 m/s.

11,168.7

A person applies an impulse of 7 kg∙m/s to a box in order to set it in motion. If the person is in contact with the box for 0.63 s, what is the average force exerted by the person on the box?

11.1

When shopping for groceries you push a shopping cart with a constant force of 15.0 N forward for a displacement of 9.8 m forward. How much work do you do on the grocery cart?

147

The pendulum illustrated above has a length of 2 m and a bob of mass 0.04 kg. It is held at an angle Ѳ, as shown, where cosѲ = 0.9. If the pendulum is released from rest, the maximum speed the bob attains is most nearly

2 m/s

A heavy cardboard box (m = 15 kg) is pushed along a 16 m long concrete driveway (μk = 0.46). The deliverer applies a force of 142 N horizontal with the ground.

2,240

Block A of mass 2.0 kg is released from rest at the top of a 3.6 m long plane inclined at an angle of 30°, as shown in the figure above. After sliding on the horizontal surface, block A hits and sticks to block B, which is at rest and has mass 3.0 kg. Assume friction is negligible. The speed of the blocks after the collision is most nearly:

2.4 m/s

A 10 N force is applied for 2 seconds. What is the change in momentum?

20 N s

The student conducts a second experiment in which the magnitude of the force exerted on block X from block Y is measured over the time in which the collision takes place. A graph of the force as a function of time is shown. In a third experiment, the student creates a collision such that the force exerted on block X from block Y is constant for 0.020 s. Which of the following constant forces, if exerted on block X from block Y, would produce the same change in momentum as is shown by the graph?

200N

How much work is done when you lift a briefcase with a constant force of [3.3, 16.4] N, as you walk [3.0, 12.8] m to a job interview?

219.82

A person of mass 60 kg sliding along level ice at a speed of 3.0 m/s collides with a second person who is initially at rest. Assume that friction is negligible. If the two people hold onto each other and their common final speed after colliding is 2.0 m/s, the mass of the second person is

30 kg

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.

4Em

What is the momentum of a 0.009 kg tranquilizer dart fired at a speed of 649 m/s. Answer: ______________ kg*m/s

5.841

Block X of mass 2 kg and block Y of unknown mass travel toward each other. An elastic collision occurs in which momentum is conserved. The graph shows the velocity of block X and of velocity of block Y as a function of time before, during, and after the collision. What is the mass of block Y?

6 kg

A student obtains data on the magnitude of force applied to an object as a function of time and displays the data on the graph above. Answer the following question for the information and diagram above. The increase in the momentum of the object between t = 0 s and t = 4 s is most nearly

60 N·s

A car, of mass 1,396 kg, is traveling at a speed of 27 miles/hour. The average braking force that brake pads give to a car is 2,354 N. How much time (in seconds) would a car going that speed make a complete stop?

7.2 s

Calculate the gravitational potential energy of a 3.7 kg block at the peak of it's ascent if it was initially thrown up into the air at a 2 m/s. There is no air resistance.

7.4

A 2 kg object travels in the positive direction across a horizontal surface with a constant speed of 10 m/s. A force is exerted on the object for 4 s, and the force increases linearly with respect to time. The table shows data about the magnitude of the applied force exerted on the object at different times. The force is exerted on the object in the opposite direction of the object's displacement. What is the change in momentum of the object?

8N⋅s in the negative direction

What is the momentum of the 93 kg hunter running at 9.76 m/s after missing the elephant?

907.68

In an experiment, a variable net force is applied to an object. A graph of the net force exerted on the object as a function of time is shown. Which of the following experiments could have been conducted to represent the variable net force shown in the graph?

A 3 kg object increases its speed from 0 m/s to 1 m/s.

An experiment is performed in which a collision occurs between cart X and cart Y. Data are collected about each cart before and after a collision takes place. Which data from the table should the student use to verify the conservation of momentum for each trial, and what is a justification for using those data?

All data are necessary to verify the conservation of momentum, because all information for each cart should be known.

A cart is moving on a level track in the positive x-direction. A force acting parallel to the x-axis is exerted on the cart. The graph above shows the net force exerted on the cart as a function of displacement. As the cart travels from x = 0 m to x = 4 m , what is the net change in the kinetic energy of the cart?

An increase of 10 J

A student on another planet has two identical spheres, each of mass 0.6 kg, attached to the ends of a rod of negligible mass. The student gives the assembly a rotation in the vertical plane and then releases it so it falls, as shown in the top figure above. Sensors record the vertical velocity of the two spheres, and the data is shown in the graph of velocity v as a function of time t. Another student wants to calculate the assembly's angular speed and the change in the linear momentum of the center of mass of the assembly between 0 s and 0.3 s. Which of these quantities can be determined using the graph?

Angular speed and change in linear momentum

A projectile fired into the air explodes and splits into two halves of equal mass that hit the ground at the same time. If the projectile had not exploded, it would have landed at point X, which is a distance R to the right of the launch point. After the explosion, one of the halves lands at point Y, which is a distance 2R to the right of the launch point. If air resistance is negligible, where did the other half land?

At the launch point

Above is a roller coaster. Throughout the path a roller coaster, the gravitational energy changes. At which point is the gravitational potential energy (Ug) the least?

B

Two blocks are on a horizontal, frictionless surface. Block A is moving with an initial velocity of v0 toward block B, which is stationary, as shown above. The two blocks collide, stick together, and move off with a velocity of v0/3 . Which block, if either, has the greater mass?

Block B

The graph above shows the speed of a truck as it moves along a straight, level road. Which of the following describe a method to determine the distance d the truck travels during the 10 s time interval shown? Select two answers.

Calculate the area under the line in the graph. Multiply the average speed of 18 m/s by the 10 s travel time.

Above is a roller coaster. Throughout the path a roller coaster, the gravitational energy changes. At which point is the gravitational potential energy (Ug) the greatest?

D

A cart of known mass moves with known speed along a level, frictionless track, as shown in the figure above. The cart hits a force sensor and rebounds. The force sensor measures the force exerted on the cart as a function of time and as a function of the position of the cart. The results will be graphed on the axes shown. Which of the two graphs can be used to determine the cart's speed after it rebounds?

Either graph 1 or graph 2 can be used.

A force of constant magnitude F and fixed direction acts on an object of mass m that is initially at rest. If the force acts for a time interval ∆t over a displacement ∆x , what is the magnitude of the resultant change in the linear momentum of the object?

F ∆t

A student must determine a nonzero change in momentum of an object for a specific interval of time. Which of the following experiments could the student conduct? Select two answer

Give a block of known mass an initial velocity so that it slides across a rough surface in front of a motion detector, slows down, and eventually stops. Use the motion detector to record the initial velocity of the block. Drop a ball of known mass above a motion detector, and

A rock and a firecracker are each thrown into the air at the same angle and with the same initial speed. The rock follows the trajectory shown above on the left. The firecracker initially follows the same trajectory as the rock but explodes into three pieces at the point indicated above on the right. Which of the following describes the motion of the center of mass of the firecracker pieces after the explosion?

It follows a path identical to the path of the rock.

The graph above shows the potential energy U of a system as one object in the system 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?

LM

What is the unit for momentum?

Ns

The equation for momentum is:

P = mv

A block of mass M = 0.10 kg is attached to one end of a spring with spring constant k = 100 N/m . The other end of the spring is attached to a fixed wall. The block is pushed against the spring, compressing it a distance x = 0.04 m. The block is then released from rest, and the block-spring system travels along a horizontal, rough track. Data collected from a motion detector are used to create a graph of the kinetic energy K and spring potential energy Us of the system as a function of the block's position as the spring expands. How can the student determine the amount of mechanical energy dissipated by friction as the spring expanded to its natural spring length?

Subtract the final kinetic energy of the block-spring system from the initial spring potential energy stored within the block-spring system.

Two blocks, of mass m and 2m, are initially at rest on a horizontal frictionless surface. A force F is exerted individually on each block, as shown. The graph shows how F varies with time t. Which block has the greatest average power provided to it between t = 0 s and t = 3 s?

The block of mass m

A cart of known mass is free to move on the frictionless track shown. The cart is released from rest at Point A and rolls freely toward Point B, without losing contact with the track. The heights of points A and B are known.

The difference between the gravitational potential energy of the Earth-cart system when the cart is at Point A and when it is at Point B

A cart travels toward the right on a track where friction between the cart and track is negligible. The momentum of the cart as a function of time is modeled in the graph. Which of the following statements are true for the time recorded? Select two answers.

The impulse delivered to the cart is nearly equal to 0.75 kg⋅m/s. The net external force exerted on the cart is nearly equal to 0.15 N.

A test car and its driver, with a combined mass of 600 kg, are moving along a straight, horizontal track when a malfunction causes the tires to stop rotating. The car skids to a halt with constant acceleration, leaving skid marks on the road during the whole time it skids. Which two of the following measurements, taken together, would allow engineers to find the total mechanical energy dissipated during the skid? Select two answers.

The length of the skid marks The coefficient of kinetic friction between the tires and the track

In an experiment, an object is released from rest near and above Earth's surface. A student must determine the relationship between the direction of the gravitational force exerted on the object and the change in momentum caused by that force. What data could the student collect to determine the magnitude and direction of the gravitational force and the change in momentum of the object? Justify your choices. Select two answers.

The mass of the object, because it is required to determine the force due to gravity exerted on the object, and the distance fallen by the object, because the force is exerted during the entire falling distance. The mass of the object, because it is required to determine the force due to gravity exerted on the object, and the velocity of the object the instant before it reaches Earth's surface, because it is required to determine the change in velocity of the object.

A block of mass M is at rest on a ramp that is inclined at an angle θ with respect to the horizontal. Frictional forces are considered to be nonnegligible. The block is pushed against a spring and then held in place. The spring is compressed a distance of x1, and the spring is not secured to the block. The block is then released from rest, travels up the incline, and comes to rest after traveling a distance D, as shown above. Which of the following claims correctly describes the energy of the system under consideration from when the block compressed the spring and when the block has traveled a distance D along the incline? Select two answers.

The mechanical energy of the system consisting of the block and Earth increases by more than zero but less than 1/2kx1^2 the mechanical energy of the system consisting of the block does not change

A stationary cart attached to a force gauge is on a straight, horizontal, frictionless track. A student uses the force gauge to move the cart, and the gauge produces the graph of force as a function of time shown above. How does the momentum of the cart change during the time interval 0 s to 20 s?

The momentum increases in magnitude at first, then decreases without reversing direction.

An object of mass m is moving in the positive x-direction with an initial speed v. Starting at time t = 0, a time-varying force F with initial magnitude F0 is exerted on the object in the positive x-direction. Measurements of the force as a function of time are represented in the graph above. Which of the following statements is true about the motion of the object between t = 0 and t = t1?

The momentum of the object has increased by approximately 1/2 F0t1.

A student plans to conduct an experiment in which the momentum of a two-object system can be determined immediately before and after a collision takes place. The student slides block X at an unknown constant speed toward an identical block, block Y, that is initially at rest, as shown in the figure. There is negligible friction between the blocks and the surface.The student uses the data collected from the experiment to create the data table. Which of the following statements is true regarding the data?

The momentum of the two-block system is not conserved because the initial momentum of the system is not equal to the final momentum of the system.

Two billiard balls of identical mass moved toward each other and collide in a perfectly elastic collision. If the initial velocities of the balls are +30 cm/s and -20 cm/s, what are the velocities of the balls after the collision?

The one originally going +30 cm/s will go -20 cm/s after the collision

An object is used in three different experiments so that a student can analyze the motion of the object when a net force is exerted on it. The data obtained from the three experiments are shown in the table. How can the student use the data to determine the relationship between the object's change in momentum and the direction of the net force exerted on the object?

The student can calculate the change in the velocity of the object for each experiment. If the object decreases its speed or changes direction, the net force changes the momentum in the opposite direction of motion. If the object increases its speed and travels in the same direction, the net force changes the momentum in the same direction of motion.

A student drops an object from rest above a force plate that records information about the force exerted on the object as a function of time during the time interval in which the object is in contact with the force plate. Which of the following measurements should the student take, in addition to the measurements from the force plate, to determine the change in momentum of the object from immediately before the collision to immediately after the collision?

The student has enough information to make the determination.

A sled slides down a hill with friction between the sled and hill but negligible air resistance. Which of the following must be correct about the resulting change in energy of the sled-Earth system?

The sum of the kinetic energy and the gravitational potential energy changes by an amount equal to the energy dissipated by friction.

An object is released from rest at a height H near and above the surface of Earth. As the object falls toward the surface, Earth's atmosphere exerts a resistive force on the object such that it reaches a terminal velocity before it reaches the ground. Which of the following claims is true? Select two answers.

The system consisting of only the object is an open system. Earth's atmosphere does negative work on the object as it falls toward the surface.

Block X slides along a horizontal surface with a speed vX toward block Y that is initially at rest, as shown in Figure 1. After block X collides with block Y, the two blocks remain stuck together and travel at a velocity of vXY, as shown in Figure 2. Frictional forces are considered to be negligible. Which of the following claims is correct regarding the momentum of the system containing only block X and the system that contains block X and block Y?

The system containing block X is an open system, and the system of both blocks is a closed system.

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?

The system is open, because a net force is exerted on the ball as it travels in a circle.

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?

The system is open, because there is a net force exerted on the block.

A block of known mass M is at rest at the base of a ramp. A second identical block of mass M travels at a known, constant velocity v0, as shown in Figure 1. The block that travels at a constant speed collides with and sticks to the first block. Both blocks slide up the ramp and travel with an unknown velocity vR at the top of the ramp, as shown in Figure 2. All frictional forces are considered to be negligible. Which quantity should the student measure, if any, to determine whether the conservation of momentum applies to the two-block system from immediately before the collision to immediately after the blocks have reached the top of the ramp while stuck together? Justify your selection.

The velocity vR of the two-block system at the top of the ramp, because this can be used to determine the final momentum of the system.

A clay ball of mass 2m is moving horizontally with speed v0 just before colliding with a block of mass m, as shown above. The block is suspended from a light string with length L. The clay sticks to the block, and the block swings up to a maximum height h0 above the block's initial position (where h0 << L). The block then oscillates about its lowest position with period T0. Which of the following quantities is the same immediately after the collision and at the instant the block reaches height h0?

Total mechanical energy of the clay-block-Earth system

Which of the following quantities is the same immediately after the collision and at the instant the block reaches height h0?

Total mechanical energy of the clay-block-Earth system

A 2 kg block is placed at the top of an incline and released from rest near Earth's surface and unknown distance H above the ground. The angle θ between the ground and the incline is also unknown. Frictional forces between the block and the incline are considered to be negligible. The block eventually slides to the bottom of the incline after 0.75 s. The block's velocity v as a function of time t is shown in the graph starting from the instant it is released. How could a student use the graph to determine the total energy of the block-Earth system?

Use with 1/2mvf^2 = 2 kg and vf equal to the final velocity of the object that can be found from the graph.

A heavy cardboard box (m = 46 kg) is pushed along a 17 m long concrete driveway (μk = 0.44). The deliverer applies a force of 217 N horizontal with the ground and the box begins at rest. Select all of the types of energy/work that you would need to consider for this problem. (Select all that apply).

Wfriction WappliedF

Two identical spaceships are traveling in deep space, far from any planets or stars. The ships travel in the same direction, with the slower one directly behind the faster one. The ships are connected by a cable attached to a spool, so that the part of the cable outside the ships can be made longer or shorter as needed. The cable is used to bring the ships to the same speed for a transfer of cargo. The graph above shows the speed of the two ships during a 10 s interval. Does at least one of the ships have its engine turned on during the time interval shown, and what evidence indicates so?

Yes, because the momentum of the two-rocket system increases.

A baseball player tackling a hockey goalie on the free-throw line is an example of what type of collision?

inelastic

A solid metal ball and a hollow plastic ball of the same external radius are released from rest in a large vacuum chamber. When each has fallen 1 m, they both have the same

speed

Which of the following is a true completion of this sentence? If the momentum of an object changes but its mass remains the same

there is a net force acting on the object its velocity is changing

Two identical objects, X and Y, move toward each other at different speeds on a horizontal surface with negligible friction, as shown in the top figure. The objects then collide elastically and move away from each other. The kinetic energy of object X as a function of time is shown in the graph. Which of the following is true of the speed vY of object Y?

vY after the collision is greater than it was before the collision.

Impulse is a _______________ quantity.

vector