4.1 4.2 4.3
A block is released from rest and slides down a frictionless ramp inclined at 30° from the horizontal. When the block reaches the bottom, the block-Earth system has mechanical energy Eo. 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
is greater than Eo
A block of mass 3 kg slides along a horizontal surface that has negligible friction except for one section, as shown above. The block arrives at the rough section with a speed of 5 m/s and leaves it 0.5 s later with a speed of 3 m/s. What is the magnitude of the work done by the frictional force exerted on the block by the rough section of the surface?
24 J
A 10 kg block is attached to a light cord that is wrapped around the pulley of an electric motor, as shown. At what rate is the motor doing work when it is pulling the block upward with an instantaneous speed of 3 m/s and an upward acceleration of 2 m/s2 ?
360 W
A graph of the net force F exerted on an object as a function of x position is shown for the object of mass M as it travels a horizontal distance 3d . Which expression represents the change in the kinetic energy of the object?
4.5Fd
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.
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?
The speed is decreasing.
A box of mass m is initially at rest at the top of a ramp that is at an angle θ with the horizontal. The block is at a height h and length L from the bottom of the ramp. The block is released and slides down the ramp. The coefficient of kinetic friction between the block and the ramp is µ. What is the kinetic energy of the box at the bottom of the ramp?
mgh
An automobile traveling on a straight, level road has an initial speed v when the brakes are applied. In coming to rest with a constant acceleration, it travels a distance x. How far would the automobile travel in coming to rest if it had the same acceleration but an initial speed 2v?
4x
A block released from rest at position A slides with negligible friction down an inclined track, around a vertical loop, and then along a horizontal portion of the track, as shown above. The block never leaves the track. The gravitational potential energy and the kinetic energy of the block are most nearly equal at which position? (Consider the potential energy to be zero at position B.)
C
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?
Graphing the force as a function of distance and calculating the area under the curve
A conveyor belt ramp of length 7m is inclined at 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 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. For the system that only includes the object, which of the following claims best describes what happens to the mechanical energy of the system while the object is moving from the bottom of the ramp to the top of the ramp?
The mechanical energy of the object is constant because the kinetic energy of the object is constant.
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 experiment is conducted such that an applied force is exerted on a 5kg object as it travels across a horizontal surface in which frictional forces are NOT considered to be negligible. A graph of the net force exerted on the object (the Applied Force) as a function of the object's distance traveled is shown. How could a student use the graph to determine the net work done on the object?
There is not enough information that is known or can be obtained from the graph to determine the net work done on the object.
The Atwood's machine shown consists of two blocks connected by a light string that passes over a pulley of negligible mass and negligible friction. The blocks are released from rest, and m2 is greater than m1. Assume that the reference line of zero gravitational potential energy is the floor. Which of the following best represents the total gravitational potential energy U and total kinetic energy K of the block-block-Earth system as a function of the height h of block m1?
U and K form trapezoid
A block of mass 10 kg moves from position A to position B shown in the figure above. The speed of the block is 10 m/s at A and 4.0 m/s at B. The work done by friction on the block as it moves from A to B is most nearly A block of mass 10 kg moves from position A to position B shown in the figure above. The speed of the block is 10 m/s at A and 4.0 m/s at B. The work done by friction on the block as it moves from A to B is most nearly
-220 J
The figure above shows the net force exerted on an object as a function of the position of the object. The object starts from rest at position x = 0 m and acquires a speed of 3.0 m / s after traveling a distance of 0.090 m. What is the mass of the object?
0.030 kg
A 4 kg block is pushed up an incline that makes a 30o 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?
100 J
A block of mass 3 kg slides along a horizontal surface that has negligible friction except for one section, as shown above. The block arrives at the rough section with a speed of 5 m/s and leaves it 0.5 s later with a speed of 3 m/s. What is the magnitude of the average frictional force exerted on the block by the rough section of the surface?
12 N
The graph above shows the force exerted by a spring as a function of the length of the spring. A block on a frictionless table is pushed against the spring that is fastened to a wall. The spring is compressed until its length is 20 cm. The block is then released. Which of the following values is closest to the kinetic energy with which the block leaves the spring?
3 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. The total energy of the object-spring system is most nearly
3.8 J
A constant force of 900 N pushes a 100 kg mass up the inclined plane shown above at a uniform speed of 4 m/s. The power developed by the 900 N force is most nearly
3600 W
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
A block released from rest at position A slides with negligible friction down an inclined track, around a vertical loop, and then along a horizontal portion of the track, as shown above. The block never leaves the track. After the block is released, in which of the following sequences of positions is the speed of the block ordered from fastest to slowest?
B E C D
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 37°. 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?
Determine final kinetic energy as described above and compare it with the initial gravitational potential energy of the block-Earth system as described above.
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 above shows the force as a function of position. What is the net work done on the object over the distance shown?
F0d
Two blocks of the same mass but made of different material slide across a horizontal, rough surface and eventually come to rest. A graph of the kinetic energy of each block as a function of position along the surface is shown. Which of the following is a true statement about the frictional force Ff that is exerted on the two blocks?
Ff2 = 2Ff1, since the force of friction is represented as the slope for each of the two curves.
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?
Increasing Increasing Constant
A student is asked to move a box from ground level to the top of a loading dock platform, as shown in the figures above. In Figure 1, the student pushes the box up an incline with negligible friction. In Figure 2, the student lifts the box straight up from ground level to the loading dock platform. In which case does the student do more work on the box, and why?
Neither method, because the work is the same in both cases, since using the ramp decreases the force by the same factor that it increases the distance
The figure above shows the paths of two stars of equal mass as they orbit their common center of mass. The positions of the stars at four different times are labeled in the figure. At which of the positions do the stars have their greatest speed?
Position 4 only
Some students want to calculate the work done by friction as an object with unknown mass moves along a straight line on a rough horizontal surface. The students have a force probe, a meterstick, and a stopwatch. Which of the following will allow the students to take the measurements needed to calculate the work done by friction?
Pulling the block at an unknown constant speed with the force probe for a measured distance
A student conducts an experiment in which an object is released from rest above a motion detector so that data can be collected about the object's motion as the object falls to the ground. The experiment is conducted near Earth's surface. All frictional forces are considered to be negligible unless otherwise stated. The student wants to collect data to determine the work done by the force due to gravity on the object as it falls. Which of the following lists contains the fewest number of measuring devices, in addition to the motion detector, that the student can use?
Spring scale
Two objects are released from rest at the top of ramps with the same dimensions, as shown in the figure above. The sphere rolls down one ramp without slipping. The small block slides down the other ramp without friction. Which object reaches the bottom of its ramp first, and why?
The block, because it does not gain rotational kinetic energy, but the sphere does
The surface of an incline is coated with an experimental substance that is intended to reduce the frictional force between a block and the surface of the incline. A 2 kg block is placed at the top of the incline at a height of 1.8 m, as shown in the figure. After the block is released from rest, the block slides down the incline and a motion detector at the bottom of the incline measures the block's speed as 5.8 m/s after the block is no longer on the incline. Which of the following claims is correct about the experimental substance?
The experimental substance did not reduce all the frictional force because some of the gravitational potential energy of the Earth-block system at the top of the incline was converted into nonmechanical energy.
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. As the crate slides a distance d, how does the new gain in kinetic energy compare to ∆K?
The new gain is less than ∆K.
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 ½ mv2f with m=2 kg and vf equal to the final velocity of the object that can be found from the graph.
The small block shown in the figure above was released from rest at point O and slid down the track such that friction was considered to be negligible. The block reached point P with speed v1. Between points O and P, what kind of work did the track do on the block, and why?
Zero work, because the track does not exert a force on the block directed along the block's direction of motion.
A student uses a spring scale to exert a horizontal force on a block, pulling the block over a smooth floor. The student repeats the procedure several times, each time pulling the block from rest through a distance of 1.0 m. For which of the following graphs of force as a function of distance will the block be moving the fastest at the end of the 1.0 m?
staircase
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
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.
A person holds a 4.0 kg block at position A shown above on the left, in contact with an uncompressed vertical spring with a spring constant of 500 N/m. The person gently lowers the block from rest at position A to rest at position B. Which of the following describes the change in the energy of the block-spring-Earth system as a result of the block being lowered?
The energy decreases by approximately 1.5 J.
Objects X and Y are connected by a string of negligible mass and suspended vertically over a pulley of negligible mass, creating an Atwood's machine, as shown in the figure. The objects are initially at rest, and the mass of Object Y is greater than the mass of Object X. As Object Y falls, how does the gravitational potential energy of the Object X-Object Y-Earth system change? All frictional forces are considered to be negligible.
The gravitational potential energy decreases because the center of mass of Object X and Object Y moves downward.
A block on a horizontal surface of negligible friction is placed in contact with an ideal spring, as shown above. The block is moved to the left so that the spring is compressed a distance x from equilibrium and then released from rest. The block has kinetic energy K1 when it separates from the spring. When the spring is compressed a distance 2x and the block is released from rest, the kinetic energy of the block when it separates from the spring is
4K1
Three identical massive bodies are at the corners of an equilateral triangle, each a distance Do from the center of mass of the other two bodies, as shown in the figure. Each body has mass M. What is the gravitational potential energy of the three-body system?
-3GCM^2/Do
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 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 cylinder at rest is released from the top of a ramp, as shown above. The ramp is 1.0 m high, and the cylinder rolls down the ramp without slipping. At the bottom of the ramp, the cylinder makes a smooth transition to a small section of a horizontal table and then travels over the edge at a height of 1.0 m above the floor, eventually landing on the floor at a horizontal distance of 1.5 m from the table. After the cylinder leaves the table, but before it lands, how do the rotational kinetic energy and translational kinetic energy of the cylinder change, if at all?
#3
Consider a system of two objects and Earth. Object X and object Y are held together by a light string as shown in the figure. MY is larger than MX. The two-object system is released from rest in the orientation shown in the figure at a height H above Earth's surface. The change in the kinetic energy of the system from when it is released to the instant it hits the ground is most nearly instant it hits the ground is most nearly.
(MY + Mx)gH
A person starting from rest at point 1 swings along a circular arc from a rope, as shown above. Point 2 is at a lower height than point 1. What is the trajectory of the person when the person lets go of the rope at Point 2?
curves are nearly symmetric
A ball is suspended by a lightweight string, as shown in the figure above. The ball is displaced to position 1 and released. The four labeled positions are evenly spaced along the arc of the ball's motion. Between which adjacent pairs of positions is the change in kinetic energy of the ball greatest?
1 and 2
A force F is exerted on a 5 kg block to move it across a rough surface, as shown above. The magnitude of the 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 kinetic energy does the block now gain as it moves a distance of 2 m?
14 J
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. For which segment does the cart move the greatest distance?
AB
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
0
A block of mass m is launched by a spring of negligible mass along a horizontal surface of negligible friction. The spring constant of the spring is k. The spring is initially compressed a distance x0. The block is released from rest. Some time after the block is released and travels in the direction shown in the figure, the spring compression is xf. Which of the following mathematical calculations can a student use to determine the speed vf of the block at this new position?
1/2kx^2O = 1/2kx^2F + 1/2mv^2f solve for vf
The pendulum shown in the figure above reaches a maximum height h above the equilibrium position as it oscillates. Assuming friction and air resistance are negligible, which of the following is true about the total energy of the Earth-pendulum system as the pendulum oscillates?
It is constant throughout the pendulum's motion.
A student conducts an experiment in which an object is released from rest above a motion detector so that data can be collected about the object's motion as the object falls to the ground. The experiment is conducted near Earth's surface. All frictional forces are considered to be negligible unless otherwise stated. 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 K and gravitational potential energy Ug of the object-Earth system as a function of time?
flat line
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. What is the magnitude of the work done by gravity as the object slides down the incline?
mgx sinθ
A child slides from rest down slides A and B shown. The slides are the same height, and the coefficient of friction between the slides and the child is the same. Which of the following compares the change ∆K in the kinetic energy of the child and the change ∆U in the potential energy of the child-Earth system for the two slides?
∆KA > ∆KB; ∆UA = ∆UB
Three identical blocks each take a different path from a height h to the ground. Block A is released from rest and falls vertically. Block B is released from rest and slides down a frictionless incline. Block C is projected horizontally with an initial speed v. Which block has the greatest speed just before hitting the ground?
Block C
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?
1.2 m
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. For another identical object initially at rest, no frictional force is exerted during segment 2 (between t = 2 s and t = 4 s). A rope exerts the same constant force of magnitude FT as in the previous scenario. What is the change in the object's kinetic energy during segment 2?
12.0 J
Figure 1 shows the kinetic energy as a function of time for a 2kg object that is released from rest and falls toward Earth's surface. Figure 2 shows the kinetic energy as a function of time for a 5kg object that is released from rest and falls toward Earth's surface. Both objects are released simultaneously from the same height. How much does the gravitational potential energy of the object-object-Earth system change from 0s to 10s ?
1400J
A 2.5 g marshmallow is placed in one end of a 40 cm pipe, as shown in the figure above. A person blows into the left end of the pipe to eject the marshmallow from the right end. The average net force exerted on the marshmallow while it is in the pipe is 0.7 N. The speed of the marshmallow as it leaves the pipe is most nearly
15 m/s
Blocks X and Y are connected by a string that passes over a pulley, as shown in the figure. Block Y has more mass than Block X. The string and pulley have negligible mass, and the pulley rotates with negligible friction. After the blocks are released from rest, what happens to the mechanical energy Emech of the system consisting of the two blocks and Earth?
Emech remains constant.
A block of mass M=0.10kg 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.
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 slides across a flat, horizontal surface to the right. For each choice, the arrows represent velocity vectors of the block at successive intervals of time. Which of the following diagrams represents the situation in which the block loses kinetic energy?
all facing right getting shorter
A conveyor belt ramp of length 7m is inclined at 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 m/s . A motor is used to keep the conveyor belt moving. The mass of the objects that are placed on the conveyor belt are varied. Suppose the motor breaks and a person must push an object of mass 30kg from the bottom of the incline to the top of the incline. The person can exert a force of 150N on the object parallel to the incline. What is the approximate amount of work that the person does on the object to move it to the top of the incline? Assume that all frictional forces are negligible.
239 J
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
An apple is released from rest 500 m above the ground. Due to the combined forces of air resistance and gravity, it has a speed of 40 m/s when it reaches the ground. What percentage of the initial mechanical energy of the apple-Earth system was dissipated due to air resistance? Take the potential energy of the apple-Earth system to be zero when the apple reaches the ground.
84%
An experiment is conducted such that an applied force is exerted on a 2kg object as it travels across a horizontal surface. A graph of the net force exerted on the object as a function of the object's distance traveled is shown. How could a student use the graph to determine the work done by the applied force?
Calculate the area bound by the line of best fit and the horizontal axis from 0m to 3m.
A student conducts an experiment in which an object is released from rest and falls to the floor. In the experiment, frictional forces CANNOT be neglected. The student uses experimental data to create two graphs. Figure 1 is a graph of kinetic energy of the object as a function of time. Figure 2 is a graph of the object-Earth system's gravitational potential energy as a function of time. How should the student use one or both graphs to determine how much the total mechanical energy changes after 5s ?
Calculate the magnitude of the difference between the final kinetic energy of the object found from the graph in Figure 1 and the initial gravitational potential energy of the object-Earth system found from the graph in Figure 2.
A student is conducting an experiment to analyze the mechanical energy of a block-spring system. The student places a block of mass 2kg on a horizontal surface and attaches the block to a horizontal spring of negligible mass and spring constant 100N/m, as shown in the figure. There is negligible friction between the block and the horizontal surface. The other end of the spring is attached to a wall. The block-spring system is initially at the spring's equilibrium position. Based on data collected from the experiment, the student creates the graph that shows the force exerted on the spring as a function of the distance the spring is compressed. How can the student use the data to experimentally determine the work done on the spring by the block?
Determine the area bound by the line of best fit through the data and the horizontal axis from 0.0 m to 1.0 m.
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?
Exponential, Exponential, Flat
An object is moving to the right with speed vi when a force of magnitude F is exerted on it. In which of the following situations is the object's direction of motion changing and kinetic energy decreasing at the instant shown?
F up and left vi forward
A student is conducting an experiment to analyze the mechanical energy of a block-spring system. The student places a block of mass 2kg on a horizontal surface and attaches the block to a horizontal spring of negligible mass and spring constant 100N/m, as shown in the figure. There is negligible friction between the block and the horizontal surface. The other end of the spring is attached to a wall. The block-spring system is initially at the spring's equilibrium position. The student wants to collect data of the block-spring system that can be used to determine the work done on the spring by the block when the spring is compressed. Which of the following includes only the measuring devices that the student will need in order to collect the data? Correct answer:
Force probe and meterstick
A ball is dropped and bounces off the floor. Its speed is the same immediately before and immediately after the collision. How does the height to which the ball bounces compare to the height from which it was dropped?
It is the same.
A planet moves in an elliptical orbit around a star, as shown in the diagram. Which of the following is true as the planet moves from position 1 to position 2?
Kinetic energy decreases and gravitational potential energy increases, but the total energy in the planet-star system stays constant.
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.
An athlete with mass m running at speed v grabs a light rope that hangs from a ceiling of height H and swings to a maximum height of h1. In another room with a lower ceiling of height H/2 , a second athlete with mass 2m running at the same speed v grabs a light rope hanging from the ceiling and swings to a maximum height of h2. How does the maximum height reached by the two athletes compare, and why?
The two athletes reach the same height, because the athletes run with the same speed.
A 2 kg object is released from rest near and above Earth's surface such that the object-Earth system's gravitational potential energy as a function of time is shown in the graph. Which of the following graphs represents the kinetic energy of the object as a function of time? Assume all frictional forces are considered to be negligible.
exponential up
A block of mass M is sliding with an initial speed vi along a horizontal surface with negligible friction. A constant force of magnitude FA is exerted on the object at an upward angle of 60o from the horizontal, causing the object to speed up. If the block remains in contact with the floor, what is the change in the block's kinetic energy as it moves a horizontal distance Δx? ½ Mvi2 + ½ FAΔx
½ FAΔx
A conveyor belt ramp of length 7m is inclined at 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 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. For the system that only includes the object, which of the following claims best describes what happens to the mechanical energy of the system while the object is moving from the bottom of the ramp to the top of the ramp? Object X and object Y are placed on the incline such that the motor moves the conveyor belt. The mass of object X is greater than the mass of object Y. After both objects have been placed on the conveyor belt and travel at a constant speed, how does the rate of change of the gravitational potential energy of the object X-Earth system per unit of time ΔUg/XΔt compare to that for the object Y-Earth system ΔUgY/Δt ?
ΔUgXΔt>ΔUgYΔt , because object X has a greater mass than object Y.
