physics

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

(My+Mx)gH

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 plane

1.25 N

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

One end of a string is attached to a vertical pole with the other end of the string attached to a ball that swings in a horizontal circular path, as shown. Which of the following free body diagrams represents the forces exerted on the ball?

110 degree angle c flipped

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. 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

An object of mass M is attached to a string of negligible mass and spun in a vertical circle of radius R, as shown in the figure above. As the object's height increases, its speed decreases such that the object-Earth system's total mechanical energy remains constant. By how much does the object's kinetic energy decrease in moving from point O, the lowest point on the circle, to point P, the highest point on the circle?

2MgR

A student rides a bicycle in a circle at a constant speed and constant radius. A force diagram for the student-bicycle system is shown in the figure above. The value for each force is shown in the figure. What is the acceleration of the student-bicycle system?

5 m/s^2

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?

A toy car that initially increases its speed, travels at a constant speed, and then decreases its speed.

Object 1 and object 2 travel across a horizontal surface, and their horizontal velocity as a function of time is shown in the graph. Which of the following statements is correct about the two-object system?

After 2s, object 1 travels a greater distance than object 2 travels.

A planet travels in an elliptical orbit around its star, as shown above. Which arrow best shows the direction of the net force exerted on the planet?

C

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 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.

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.

During an experiment, a block of mass M=0.20kg is placed on a disk that rotates about an axle through its center, as shown in the diagram. The block is moved to different distances R from the axle, and the tangential speed of the block is gradually increased until the mass begins to slip. The distance and maximum tangential speed before slipping, vmax, are recorded. A student creates a graph of vmax2 as a function of R, as shown. How should the student use the graph to most accurately determine the experimental value of the coefficient of static friction μS between the block and the disk?

Determine the slope of the best fit line and set it equal to μSg.

A student wants to investigate the motion of a ball by conducting two different experiments, as shown in Figure 1 and Figure 2 above. In Experiment 1, the student releases a ball from rest and uses a slow-motion camera to film the ball as it falls to the ground. Using video analysis, the student is able to plot the ball's horizontal position x and vertical position y as a function of time t. In Experiment 2, the student horizontally rolls the same ball off a table, and uses video analysis to plot the ball's horizontal position x and vertical position y as a function of time t starting from the instant the ball leaves the table. The graphs from each experiment are shown above along with each graph's best-fit curve line. Suppose that Experiment 1 and Experiment 2 are conducted at the same time; one student drops the ball from rest at the same instant that a second student horizontally rolls an identical off the table. After both balls have traveled half their vertical distance to the floor, what is the acceleration of the center of mass of the two-ball system relative to Earth?

Equal to g

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.

The diagram above represents the forces exerted on a box that a child is holding. FNrepresents the force applied by the child's hand, and Fg represents the weight of the box. The child begins to raise the box with increasing speed. Which of the following claims is correct about force Fh that is exerted by the box on the child's hand as the box is being raised?

Fh=FN, where FN is larger as the box is being raised than when it was being held.

wo 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. If the net acceleration is downward but has a magnitude less than g, then which has the larger magnitude, the force F or the tension in the rope?

Force F

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?

Force probe and meterstick

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.

Two students wish to determine the value of g, the acceleration due to gravity at Earth's surface. The students have a collection of blocks of different masses, a string of negligible mass, a pulley of negligible mass, and a device for measuring acceleration. The students attach two of the blocks to the ends of the string and pass the string over the pulley so the blocks hang vertically on either side. The blocks are then released from rest, and their acceleration is measured. The students' data for one trial are shown below, with m1 and m2 equal to the masses of the blocks. Considering the gravitational forces acting on the blocks, do the data provide a reasonable determination of the value of g, and what is a possible justification for why or why not?

No, because the calculated value of g is too small, possibly due to an additional force exerted on the blocks-string system.

Two bricks are stacked on a floor. A student draws the force diagram for brick 2, as shown above. The forces are an upward normal force, a downward force exerted by brick 1, and a downward gravitational force. How many of the forces, if any, in the force diagram are contact forces caused by microscopic interactions?

Only two

Identical spheres are dropped from a height of 100 m above the surfaces of Planet Xand Planet Y. The speed of the spheres as a function of time is recorded for each planet in the graph above. Which planet exerts the greater force of gravity on the sphere, and what evidence supports this conclusion?

Planet X, because its line has the greater slope.

A student wants to investigate the motion of a ball by conducting two different experiments, as shown in Figure 1 and Figure 2 above. In Experiment 1, the student releases a ball from rest and uses a slow-motion camera to film the ball as it falls to the ground. Using video analysis, the student is able to plot the ball's horizontal position x and vertical position y as a function of time t. In Experiment 2, the student horizontally rolls the same ball off a table, and uses video analysis to plot the ball's horizontal position x and vertical position y as a function of time t starting from the instant the ball leaves the table. The graphs from each experiment are shown above along with each graph's best-fit curve line. Which of the following conclusions can the student draw from the graphs, and why?

Since the balls have the same vertical position at any given time, they reach the ground at the same time.

A block of mass M and a block of mass 3M are connected by a string, as shown above. The blocks are held with the string horizontally and are released from rest at the same time from a height Habove the ground. How does the acceleration of the center of mass of the system compare to the acceleration of the object of mass M ?

The acceleration of the center of mass is the same as the acceleration of the object of mass M.

Two spheres of mass M and 2M float in space in the absence of external gravitational forces, as shown in the figure. Which of the following predictions is correct about the motion of the center of mass of the two-sphere system?

The center of mass remains at rest.

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 5.8ms 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 tennis ball is thrown against a vertical concrete wall that is fixed to the ground. The ball bounces off the wall. How does the force exerted by the ball on the wall compare with the force exerted by the wall on the ball?

The forces exerted by the ball and the wall have the same magnitude.

A ball of mass m is found to have a weight Wx on Planet X. Which of the following is a correct expression for the gravitational field strength of Planet X?

The gravitational field strength of Planet X is Wx/m.

A space station has a mass M and orbits Earth in a circular orbit at a height above Earth's surface. A payload of mass m, where m<M, is delivered to the space station. Soon after, the space station's orbit is adjusted so that it is 50 km farther away from Earth's surface than before. Which of the following best describes the effects of these changes on Earth's gravitational field strength at the space station's new location?

The increase in mass of the space station has no effect on the field strength, and the increase in orbital radius decreases the field strength.

A ball is dropped onto the floor and bounces upward. Which of the following claims are correct about the force that the ball exerts on the floor compared to the force that the floor exerts on the ball when the ball and the floor are in contact?

The magnitude of the forces exerted by both objects is the same because the ball and the floor cannot exert forces of different magnitudes on each other.

A satellite of mass m orbits a moon of mass M in uniform circular motion with a constant tangential speed of v. The figure shows the net force exerted on the satellite by the moon and the direction of the tangential velocity of the satellite at time t0. Which of the following statements is true regarding the motion of the satellite?

The tangential velocity of the satellite does not remain 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 cart with an unknown mass is at rest on one side of a track. A student must find the mass of the cart by using Newton's second law. The student attaches a force probe to the cart and pulls it while keeping the force constant. A motion detector rests on the opposite end of the track to record the acceleration of the cart as it is pulled. The student uses the measured force and acceleration values and determines that the cart's mass is 0.4kg. When placed on a balance, the cart's mass is found to be 0.5kg. Which of the following could explain the difference in mass?

The track was not level and was tilted slightly downward.

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 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.

An object is released from rest near and above Earth's surface from a distance of 10m. After applying the appropriate kinematic equation, a student predicts that it will take 1.43s for the object to reach the ground with a speed of 14.3m/s . After performing the experiment, it is found that the object reaches the ground after a time of 3.2s. How should the student determine the actual speed of the object when it reaches the ground? Assume that the acceleration of the object is constant as it falls.

Use y = y0+vy0t+12ayt2 to determine the acceleration of the object as it falls since all other quantities are known. Then use mgy0−WExternal = 12mv2f with WExternal = may(yf−y0) since all other quantities are known. Solve for vy .

Two students want to determine the speed at which a ball is released when thrown vertically upward into the air. One student throws the ball into the air while the other student measures the total time that the ball is in the air. The students use a meterstick to measure the release height of the ball. Which of the following equations should the students use to determine the speed at which the ball was released?

Use y=y0+vy0t+12ayt2 from the moment in time in which the ball was released to the moment in time in which the ball hits the ground.

Identical objects, object X and object Y, are tied together by a string and placed at rest on an incline, as shown in the graph. The string has a length of 2 m. The system of the two objects is released from rest, and a graph of the velocity of the center of mass of the system as a function of time is shown in the figure. If the string was cut and object Y was released from rest while object X was held at rest, which of the following claims is correct about the new acceleration of the center of mass of system anew compared to the original acceleration of the center of mass of the system aoriginal ?

anew will be less than aoriginal

Block X of mass M is attached to block Y of mass 2M by a light string that passes over a pulley of negligible friction and mass, as shown above. In which direction will the center of mass (COM) of the two-block system move after it is released from rest, and what is the magnitude of the acceleration a of block X ?

com down right a 2g/3

A student wants to launch a toy dart toward a target that hangs from a light string. At time t=0, the dart is launched with an initial speed v0 at an angle θ0above the horizontal ground. At the instant the dart is launched, the string is cut such that the target begins to fall straight down. The positive horizontal direction is considered to be to the right, and the positive vertical direction is considered to be up. Which of the following graphs could represent the vertical component of the velocity as a function of time for the dart and the target immediately after the dart is launched and the target begins to fall?

dart positive (negative slope) target 0 (negative slope)

A student wants to launch a toy dart toward a target that hangs from a light string. At time t=0, the dart is launched with an initial speed v0 at an angle θ0 above the horizontal ground. At the instant the dart is launched, the string is cut such that the target begins to fall straight down. The positive horizontal direction is considered to be to the right, and the positive vertical direction is considered to be up. Figure 1 shows a displacement-versus-time graph for the dart. Figure 2 shows a displacement-versus-time graph for the target. For both graphs, the component of the displacement is not indicated.Which displacement component, horizontal or vertical, is represented by the graph for each object?

dart vertical, target vertical

A block of mass M=0.10kg is attached to one end of a spring with spring constant k=100Nm . The other end of the spring is attached to a fixed wall. The block is pushed against the spring, compressing it a distance x=0.04m . 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?

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

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?

μkm2g/(m1+m2)

A student wants to launch a toy dart toward a target that hangs from a light string. At time t=0, the dart is launched with an initial speed v0 at an angle θ0above the horizontal ground. At the instant the dart is launched, the string is cut such that the target begins to fall straight down. The positive horizontal direction is considered to be to the right, and the positive vertical direction is considered to be up. A student makes the necessary measurements to create the graph shown, which represents the vertical component of the velocity as a function of time for the dart and for the target from t=0 until the instant the dart hits the target. At t=0, the target is a vertical distance h above the dart. The curves for the dart and the target each have the same area between them and the horizontal axis. Both curves also have the same slope. Which of the following is the best method to determine the distance h from the graph?

Find twice the area under the curve for the dart's data.

A car initially at rest accelerates at 10ms2. The car's speed after it has traveled 25meters is most nearly

22 m/s

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?

-10 m

A potato falling vertically downward is struck by a dart that is traveling vertically upward, as shown above. The dart and potato then collide, stick together, and continue moving after the collision. Consider the dart-potato system. Which of the following graphs best represents the speed v of the center-of-mass of the dart-potato system, as a function of time t, before, during, and after the collision?

/

An object is sliding to the right along a straight line on a horizontal surface. The graph shows the object's velocity as a function of time. What is the object's displacement during the time depicted in the graph?

0 m

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 ms. 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?

0.72 N

An Atwood machine is set up by suspending two blocks connected by a string of negligible mass over a pulley, as shown in the figure above. The pulley has negligible mass but there is friction as it rotates. The system is released from rest, and after 1.0 s the speed of the 3 kg block is 1.8 m/s. Which of the following is the best estimate of the external frictional force acting on the two-block system?

1 N

At time t=0, a moving cart on a horizontal track is at position 0.5m. Using a motion detector, students generate a graph of the cart's velocity as a function of time, as shown above. At t=2.5s, the cart's position is most nearly

1.75 m

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 60∘ 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 ?

1/2 FA delta x

An object is dropped from the top of a building near Earth's surface. After 2 s, a second identical object is dropped from the same building from the same height. After 4 s, the first object strikes the ground. The graph shows the speeds ν of both objects as a function of time t. What is the approximate acceleration of the center of mass of the two-object system at the moment right before the first object reaches the ground?

10 m/s^2

The figure above shows the forces exerted on a block that is sliding on a rough horizontal surface: The weight of the block is 500 N, the normal force is 500 N, the frictional force is 100 N, and there is an unknown force F exerted to the right. The acceleration of the block is 0.4 m/s2. The value of F is most nearly

120 N

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?

12kx20=12kx2f+12mv2f. Solve for vf.

The free body diagram shown above is for a 5 kg box on a rough surface being pulled to the right at a constant speed by a string that is at an angle of 30° above the horizontal. The coefficient of kinetic friction between the box and the surface is 0.30. The tension in this string is most nearly

14.47 N

A ball is attached to one end of a string such that the ball travels in a vertical circular path near Earth's surface. The force diagram of the ball at its lowest point in the circular path is shown above. What is the net centripetal force exerted on the ball?

15 N

An object is released from rest near the surface of a planet. The velocity of the object as a function of time is expressed in the following equation. vy=(−3ms2)t All frictional forces are considered to be negligible. What distance does the object fall 10 s after it is released from rest?

150 m

A moon of mass 1×1020kg is in a circular orbit around a planet. The planet exerts a gravitational force of 2×1021N on the moon. The centripetal acceleration of the moon is most nearly

20 m/s^2

An object of mass 10 kg is released from rest above the surface of a planet such that the object's speed as a function of time is shown by the graph above. The force due to gravity exerted on the object is most nearly

35 N

A 2 kg object is a distance of 10,000,000 m away from the center of Earth, which has a mass of nearly 6×1024 kg. What is the approximate gravitational field strength of Earth's gravitational field at the location of the 10 kg object?

4 N/kg

An Atwood's machine is set up by suspending two blocks connected by a string of negligible mass over a pulley, as shown above. The blocks are initially held at rest and then released at time t0=0 s. The speed of the 3 kg block at time t1=2.0 s is most nea 4 m

4 m/s

A 10kg object is near a planet's surface such that the gravitational field strength is 4Nkg. With what force is the planet attracted to the 10kg object?

40 N

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 ball of mass M is on a horizontal surface with negligible friction. One end of a string is attached to the ball so that it is spun in a horizontal circle of radius R at tangential speed v0, as shown in Figure 1. A free-body diagram for the ball at an instant in time is shown in Figure 2. The magnitude of the tension force is also indicated in Figure 2. Which of the following equations represents the centripetal acceleration of the ball if its tangential speed is increased to 2v0?

4v^2 / R

A student wants to investigate the motion of a ball by conducting two different experiments, as shown in Figure 1 and Figure 2 above. In Experiment 1, the student releases a ball from rest and uses a slow-motion camera to film the ball as it falls to the ground. Using video analysis, the student is able to plot the ball's horizontal position x and vertical position y as a function of time t. In Experiment 2, the student horizontally rolls the same ball off a table, and uses video analysis to plot the ball's horizontal position x and vertical position y as a function of time t starting from the instant the ball leaves the table. The graphs from each experiment are shown above along with each graph's best-fit curve line. In Experiment 1, what is the speed of the ball the instant it makes contact with the ground?

5.4 m/s

A satellite of mass 1000 kg is in a circular orbit around a planet. The centripetal acceleration of the satellite in its orbit is 5 ms2. What is the gravitational force exerted on the satellite by the planet?

5000 N

A 2kg object is released from rest near the surface of a planet such that its gravitational field is considered to be constant. The mass of the planet is unknown. The object's speed after falling for 3 s is 75 m/s. Air resistance is considered to be negligible. Calculate the weight of the 2kg object on the planet of unknown mass.

50N

A ball is released from rest from the twentieth floor of a building. After 1 s, the ball has fallen one floor such that it is directly outside the nineteenth-floor window. The floors are evenly spaced. Assume air resistance is negligible. What is the number of floors the ball would fall in 3s after it is released from the twentieth floor?

7 to 10 floors

A student must determine the inertial mass of a block that is pulled across a horizontal surface using a force probe and 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?

Calculate the slope.

An astronaut with mass MA is within a satellite that orbits Earth at a height H above its surface. Earth has a mass ME and radius RE. Which of the following is a correct expression for the gravitational force exerted on the astronaut by Earth?

G*(MEMA/(RE+H)^2)

A cart of mass m is moving with speed v on a smooth track when it encounters a vertical loop of radius R, as shown above. The cart moves along the inside of the entire loop without leaving the track. All frictional forces are negligible. Which of the following free-body diagrams shows the force or forces exerted on the cart at point Q ?

L shape normal and gravity

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

No, because the moon's distance from the planet is always changing.

A student must determine the relationship between the inertial mass of an object, the net force exerted on the object, and the object's acceleration. The student uses the following procedure. The object is known to have an inertial mass of 1.0kg. Step 1: Place the object on a horizontal surface such that frictional forces can be considered to be negligible. Step 2: Attach a force probe to the object. Step 3: Hang a motion detector above the object so that the front of the motion detector is pointed toward the object and is perpendicular to the direction that the object can travel along the surface. Step 4: Use the force probe to pull the object across the horizontal surface with a constant force as the force probe measures force exerted on the object. At the same time, use the motion detector to record the velocity of the object as a function of time. Step 5: Repeat the experiment so that the object is pulled with a different constant force. Can the student determine the relationship using this experimental procedure?

No, because the motion detector should be oriented so that the object moves parallel to the line along which the front of the motion detector is aimed.

An astronaut in deep space is at rest relative to a nearby space station. The astronaut needs to return to the space station. A student makes the following claim: "The astronaut should position her feet pointing away from the space station. Then, she should repeatedly move her feet in the opposite direction to each other. This action will propel the astronaut toward the space station." Is the student's claim correct? Justify your selection.

No. The astronaut's feet are not exerting a force on another object, so there is no external force to accelerate the astronaut toward the space station.

A spaceship travels from a planet to a moon and passes through the three positions A, B, and C, shown above. Position B is midway between the centers of the planet and the moon. The planet has a larger mass than the moon. At which location could the net gravitational force exerted on the spaceship be approximately zero?

Position C

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 xf in relation to the starting position x0 and the student's average horizontal acceleration axbetween 0.0 s and 3.0s?

Position xf is farther away from the sensor than x0, and ax is negative.

An object of mass M1 travels in a circular path of radius R on a horizontal table. The object is attached to a string that passes through a hole in the center of the table. An object of mass M2 is attached to the other end of the string and hangs vertically under the table, which produces a force on M1. All frictional forces are considered to be negligible. Which quantity or quantities must be measured to determine the tangential speed required to keep the system in equilibrium?

R, M1, M2

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?

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?

Tcos(θ)−μ(Mg−Tsin(θ))M

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. If F=300 N, which of the following predictions about the acceleration of the two-block system is correct?

The acceleration is upward with a magnitude of g.

Object A of mass 2kg is gravitationally attracted to object B of mass 2kg as the two objects float in space. Frictional forces are negligible. The gravitational forces of attraction between the two objects are shown in the table above. Which of these claims about the motion of the center of mass of the two-object system is true?

The center of mass will not accelerate.

A book is at rest on the top of a table. A student makes the following claim: "An attractive electromagnetic force is exerted on the book from the table, and this force can also be classified as the normal force." Which of the following statements correctly justifies the student's claim?

The claim is incorrect because the charged particles of the table exert an upward repulsive force on the charged particles of the book.

A moon orbits an isolated planet in deep space. Which of the following forces that the planet exerts on the moon can be considered as negligible?

The electric force

A space station has a mass M and orbits Earth in a circular orbit at a height above Earth's surface. An astronaut in the space station appears weightless because the astronaut seems to float. Which of the following claims is true about the force exerted on the astronaut by Earth?

The force exerted on the astronaut by Earth is equal to the force exerted on Earth by the astronaut.

An astronaut stands on the surface of an asteroid. The astronaut then jumps such that the astronaut is no longer in contact with the surface. The astronaut falls back down to the surface after a short time interval. Which of the following forces CANNOT be neglected when analyzing the motion of the astronaut?

The gravitational force between the astronaut and the asteroid

A planet has two moons, Moon A and Moon B, 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 ?

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 .

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 cart of mass m is moving with speed v on a smooth track when it encounters a vertical loop of radius R, as shown above. The cart moves along the inside of the entire loop without leaving the track. All frictional forces are negligible. Which of the following must be true for the cart to remain on the track when it is at point P ?

The net force exerted on the cart must be equal to or greater than the weight of the cart.

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?

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.

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.

Students work together during an experiment about Newton's laws. The students use a setup that consists of a cart of known mass connected to one end of a string that is looped over a pulley of negligible friction, with its other end connected to a hanging mass. The cart is initially at rest on a horizontal surface and rolls without slipping when released. The inertia of the cart's wheels is negligible. Students have access to common laboratory equipment to make measurements of components of the system. The students double the mass that hangs from the string. They also replace the original cart with a new cart that has double the mass. By doubling both masses, how will the tension in the string and the acceleration of the cart change?

The tension will double, but the acceleration will stay the same.

n one experiment, a student rolls a 2 kg ball such that it collides with a wall with a force of 10,000 N. In a second experiment, the student rolls a 5 kg ball such that it collides with the wall at a force of 5000 N. In both experiments, the balls bounce back from the wall and eventually come to rest. Which of the following statements is true regarding the force that the wall exerts on each ball?

The wall exerts a greater force on the 2 kg ball than on the 5 kg ball since the force from the wall on each ball is equal to the force that each ball exerts on the wall.

A comet passes by a planet with a speed vo such that the comet travels in a straight line at the instant shown in the figure. The comet's tangential acceleration, centripetal acceleration, and force due to gravity from the planet at this location are provided in the table. Astronomers observe that the comet continues to travel in a nearly straight line, even though calculations show that the gravitational force exerted by the planet should cause the comet to move in a circular orbit. Why does the comet not travel in a circular path around the planet after the instant shown in the figure?

There must be another object such that the gravitational forces exerted on the comet are balanced at this location.

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. In what direction is the net force exerted on the moon?

Toward the planet

A student is tasked with using a force table to balance a small ring in the center of a pin, as shown in Figure 1. For each of the four strings shown, one end is attached to the small ring, and the other end is attached to a hanger that can hold masses. Each string is wrapped around a pulley so that the hanger and masses are at rest. The location of each pulley may be changed. Figure 2 shows a top-down view of the free-body diagram of the forces exerted on the pin at a particular moment in time. From a top-down perspective, in what direction will the pin accelerate?

Up and to the left

An object is thrown upward with a speed of 20m/s near the surface of a planet where the gravitational field strength is a constant magnitude of 6N/kg. The vertical position versus time of the object is shown in the graph. Is the object considered to be in free fall?

Yes, because the only force exerted on the object is the force due to gravity from the planet.

Two experiments are performed on an object to determine how much the object resists a change in its state of motion while at rest and while in motion. In the first experiment, the object is pushed with a constant known force along a horizontal surface. There is negligible friction between the surface and the object. A motion sensor is used to measure the speed of the object as it is pushed. In a second experiment, the object is tied to a string and pulled upward with a constant known force, and a motion sensor is used to measure the speed of the object as it is pulled upward. The student uses the data collected from the motion sensor to determine the mass of the object in both experiments. Which of the following classifies the type of mass that was determined in each experiment?

experiment 1 inertial experiment 2 gravitational

A solid disk of diameter D spins counterclockwise about its center at a constant speed. One end of a string of length l is attached to the edge of the disk with the other end attached to an object of mass M. At time t0, as the disk spins, the string makes an angle θ with respect to the vertical, as shown in Figure 1. A force diagram of all of the forces exerted on the object at time t0 are shown in Figure 2. The direction of the centripetal acceleration of the object at t0 is shown in Figure 3. What is the magnitude of the acceleration of the object of mass M at time t0?

g tan theta

A satellite of mass m orbits a moon of mass M in uniform circular motion with a constant tangential speed of v. The gravitational field strength at a distance R from the center of moon is gR. The satellite is moved to a new circular orbit that is 2R from the center of the moon. What is the gravitational field strength of the moon at this new distance?

gR/4

A ball is moved from Earth to a planet that has a gravitational acceleration that is double that of Earth. How does the gravitational force on the ball when it is on the new planet compare to the gravitational force on the ball when it is on Earth?

he gravitational force on the ball when it is on the new planet is double the force on the ball when it is on Earth.

A potato falling vertically downward is struck by a dart that is traveling vertically upward, as shown above. The dart and potato then collide, stick together, and continue moving after the collision. The weight of the dart is W. Which of the following claims best describes the magnitude of the net force on the dart immediately before, during, and immediately after the collision with the potato?

it is equal to W just before the collision, greater than W during the collision, and equal to W again after the collision.

An object slides across a horizontal surface such that it slows down due to the force of friction that is exerted on the object. The object and the direction of its displacement are shown in the figure. Which of the following free-body diagrams could represent the forces that are exerted on the object?

left friction, up normal, down gravity of equalness

A block is pulled along a surface of negligible friction by a spring scale that exerts a force F on the block. The mass of the block is 4kg, and the spring scale reads 10N. Which of the following free-body diagrams can be used to show the magnitude and direction of all the forces exerted on the block as it is pulled along the surface?

long normal long gravity short spring

Students work together during an experiment about Newton's laws. The students use a setup that consists of a cart of known mass connected to one end of a string that is looped over a pulley of negligible friction, with its other end connected to a hanging mass. The cart is initially at rest on a horizontal surface and rolls without slipping when released. The inertia of the cart's wheels is negligible. Students have access to common laboratory equipment to make measurements of components of the system. By collecting the appropriate data, the students can determine the relationship between the acceleration of the cart and the net force exerted on the cart. Which of the following graphs should the students produce to show the correct relationship?

positive slope straight line /

A satellite is a large distance from a planet, and the gravitational force from the planet is the only significant force exerted on the satellite. The satellite begins falling toward the planet, eventually colliding with the surface of the planet. As the satellite falls, which of the following claims is correct about how the force that the planet exerts on the satellite Fps changes and how the force that the satellite exerts on the planet Fsp changes, if at all? What reasoning supports this claim?

ps and Fsp both increase. The gravitational forces that two objects exert on one another decrease as the separation between the objects increases, and these forces are always equal in magnitude.

A ball of mass M swings in a horizontal circle at the end of a string of radius R at a constant tangential speed v0. A student gradually pulls the string inward such that the radius of the circle decreases while keeping the tangential speed v0 of the ball constant, as shown above. Which of the following graphs best represents the acceleration a of the ball as a function of time t?

second part of u shape

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 Ffexerted on the block is true?

t is the sum of all the microscopic contact forces between the bottom of the block and the surface.

A ball is swung in a vertical circle such that at one point along its circular path the forces exerted on the ball can be represented by the free body diagram. The magnitude of the tension force exerted on the ball, T, is twice that of the force due to gravity exerted on the ball from Earth, Fg. What is the location of the ball, and what is the magnitude of the centripetal acceleration of the ball

top of circle, 3g

A block is moving horizontally with a speed of v0 when it encounters a ramp, as shown above. Which of the following graphs best represents the position of the block measured from the top of the ramp as a function of time if friction is negligible?

u shaped second part

Three identical blocks, X, Y, and Z, hang from identical strings, as shown in the figure. Which of the following free-body diagrams could represent the forces exerted on block Y?

up tension long down tension down gravity of equalness

A bowling pin is thrown vertically upward such that it rotates as it moves through the air, as shown in the figure. Initially, the center of mass of the bowling pin is moving upward with a speed vi of 10 ms. The maximum height of the center of mass of the bowling pin is most nearly

vi^2 / 2g