physics
An object rotates at various distances from the center of a disk such that the object experiences a force of friction from the disk. Data collected from the experiment are shown in the table above. Each location of the disk rotates such that the tangential speed at that point remains constant. What is the magnitude of the force of friction exerted on the object if its mass is doubled and it is placed at a distance of 0.6 m from the disk's center?
3.6N
The graph above shows velocity v as a function of time t for a 0.50 kg object traveling along a straight line. The graph has three segments labeled 1, 2, and 3. A rope exerts a constant force of magnitude FT on the object along its direction of motion the whole time. During segment 2 only, a frictional force of magnitude Ff is also exerted on the object. Which of the following expressions correctly relates the magnitudes Ff and FT?
FT < Ff < 2FT
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.
A spaceship is traveling from Earth to the Moon. Which of the following is true of the gravitational force on the ship due to the two objects when the ship is equidistant from Earth and the Moon?
There is a net force because the force exerted by Earth is greater than that exerted by the Moon.
A 50.0 N box is at rest on a horizontal surface. The coefficient of static friction between the box and the surface is 0.50, and the coefficient of kinetic friction is 0.30. A horizontal 20.0 N force is then exerted on the box. The magnitude of the acceleration of the box is most nearly
0
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 kgblock 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
An object is released from rest near the surface of a planet. The vertical position of the object as a function of time is shown in the graph. All frictional forces are considered to be negligible. The strength of the gravitational field is most nearly
6
A 0.5kg object is in free fall as it falls downward near the surface of a planet. A graph of the object's velocity as a function of time is shown. What is the force due to gravity exerted on the object by the planet?
1.25N
A uniform spool is suspended from a vertical wall by a string attached to the spool's thin axle. The axle is horizontal, as shown above. The wall is smooth, so it exerts no frictional force on the spool. The tension in the string is 2.6 N. What is the weight of the spool?
2.4N
The stacks of boxes shown in the figure above are inside an elevator that is moving upward. The masses of the boxes are given in terms of the mass M of the lightest box. Assume the elevator has upward acceleration a, and consider the stack that has two boxes of mass M. What is the magnitude of the force exerted on the top box by the bottom box?
M (a + g)
A box of mass m is on a rough inclined plane that is at an angle θ with the horizontal. A force of magnitude F at an angle Φ with the plane is exerted on the block, as shown above. As the block moves up the plane, there is a frictional force between the box and the plane of magnitude f. What is the magnitude of the net force acting on the box?
F cosΦ - mg sin θ - f
Planet 1 orbits Star 1 and Planet 2 orbits Star 2 in circular orbits of the same radius. However, the orbital period of Planet 1 is longer than the orbital period of Planet 2. What could explain this?
Star 1 has less mass than Star 2.
An astronaut in the space station appears weightless because the astronaut seems to float. Which of the following claims is true about the force exerted on the astronaut by Earth?
The force exerted on the astronaut by Earth is equal to the force exerted on Earth by the astronaut.
A 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?
ac=4vo^2/R
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?
divided by re+h and squared
A rock attached to a string swings in a vertical circle, as shown above, with negligible air resistance. Which of the following diagrams could correctly show all the forces on the rock when the string is in the position above?
down and to the left
A car with speed v and an identical car with speed 2v both travel the same circular section of an unbanked road. If the frictional force required to keep the faster car on the road without skidding is F, then the frictional force required to keep the slower car on the road without skidding is
E) F/4
A 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. What additional information is needed to determine the time required for one of the moons to make one complete revolution around the planet?
The distance between the center of each moon and the planet.
A ladder at rest is leaning against a wall at an angle. Which of the following forces must have the same magnitude as the frictional force exerted on the ladder by the floor?
The normal force exerted on the ladder by the wall
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
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?
intertial mass, gravitational mass
A 2kg object is initially at rest at time t=0s. It then slides across a rough, horizontal surface under the influence of only the four forces shown in the table above. What is the speed of the object at time t=3s ?
36
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.
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.
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 ?
down and to the right, 2g/3
Two blocks of masses 1.0 kg and 2.0 kg, respectively, are pushed by a constant applied force Facross a horizontal frictionless table with constant acceleration such that the blocks remain in contact with each other, as shown above. The 1.0 kg block pushes the 2.0 kg block with a force of 2.0 N. The acceleration of the two blocks is
1
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
An object of unknown mass is swung in a vertical circle at the end of a light string, as seen in the figure above. A measurement is made of the object's tangential speed at the bottom circular path. A student must determine the tension in the string at the bottom of the circular path. Which of the following measurements, in conjunction with the object's tangential speed, are required to determine the tension in the string? Select two answers.
mass and diameter
A spacecraft is placed in a circular orbit around a planet with mass 6.4 x 1023 kg. The spacecraft orbits at a height of 4.5 x 107 m above the planet's surface. What additional information is needed to calculate the speed of the spacecraft in the orbit?
the planets radius only
The horizontal wire shown on the right in the figure above will break when the tension in it exceeds the value Tmax. What is the maximum mass M that the hanging object can have without the horizontal wire breaking? (Assume the wire on the left does not break prior to the horizontal wire breaking.)
t max tan theta/g
An object is dropped near the surface of a planet such that the gravitational field at the object's location is 8 Nkg. If the object is thrown upward at a speed of 20 ms, what is the position of the object in relation to the position in which the object was released and thrown upward after 3s ?
24
Blocks A and B, of masses m and 2m, respectively, are connected by a light string and pulled across a surface of negligible friction with a constant force F1, as shown above. The acceleration of the blocks is a. The force of the string pulling block B forward has magnitude F2. Which of the following claims correctly describes the relationship between the magnitude of the forces acting on the blocks?
F1 is greater than F2
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 builds the apparatus shown above. A light string is attached to an object of unknown mass and passed through a tube such that the other end of the string is attached to a second object of mass M. By holding on to the tube, the student swings the object of unknown mass in a horizontal circle of radius r while the object of mass M hanging from the string remains at a constant height. In each trial, the radius r of the circular path is changed and the tangential speed ν of the object of unknown mass is calculated. How can the student determine the value of the unknown mass by using the radius of its circular path and its speed?
Use the slope of a graph of R as a function of ν2.
Box A of mass m sits on the floor of an elevator, with box B of mass 2m on top of it, as shown in the figure above. The elevator is moving upward and slowing down. FA is the magnitude of the force exerted on box A by box B, FB is the magnitude of the force exerted on box B by box A, and Fg is the magnitude of the gravitational force exerted on box B. Which of the following ranks the forces in order of increasing magnitude?
(FB = FA) < Fg
To analyze the characteristics and performance of the brakes on a 1500 kg car, researchers collected the data shown in the table above. It shows the car's speed when the brakes are first applied and the corresponding braking distance required to stop the car. The magnitude of the average braking force on the car is most nearly
12,000 N
A satellite of mass m orbits a moon of mass M in uniform circular motion with a constant tangential speed of v. The satellite orbits at a distance R from the center of the moon. Which of the following is a correct expression for the time T it takes the satellite to make one complete revolution around the moon?
2pi times square root of R ^3 divided by GM
Block A and block B move toward each other on a level frictionless track. Block A has mass mand velocity +v . Block B has mass 2m and velocity -v . The blocks collide, and during the collision the magnitude of the net force exerted on block A is F. What is the magnitude of the net force exerted on block B, and why does it have that value?
F, because the net force is equal to the mutual contact force between the blocks.
A student builds the apparatus shown. One end of a light string is attached to an object of mass m0, and the other end of the string is passed through a tube and attached to a second object of mass M. The student holds on to the tube and swings the object of mass m0 in a horizontal circle while the object of mass M remains at a constant height. The time it takes for the object of mass m0 to travel around its circular path is T. Which of the following options represents the essential measuring devices needed by the student to collect the necessary data to experimentally determine the gravitational field strength of the object of mass m0 due to Earth's gravitational field?
Mass balance, meterstick, and timer
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 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.
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 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?
The 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 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 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
The inclined plane in the figure above has two sections of equal length and different roughness. The dashed line shows where section 1 ends and section 2 begins. A block of mass M is placed at different locations on the incline. The coefficients of kinetic and static friction between the block and each section are shown in the table below. If the block is sliding up section 2, what is the magnitude of the force of friction that is exerted on the block by the incline?
2 μk Mg cos θ
Identical spheres are dropped from a height of 100 m above the surfaces of Planet X and 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 planet travels in an elliptical path around a star, as shown in the figure. As the planet gets closer to the star, the gravitational force that the star exerts on the planet increases. Which statement of reasoning best supports and correctly identifies what happens to the magnitude of the force that the planet exerts on the star as the planet gets closer to the star?
The force increases because it is part of a Newton's third law pair of forces with the force that the star exerts on the planet.
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 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. How does the new normal force exerted on the crate compare to FN ?
The new normal force is less than FN.
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?
Fps 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.
Two blocks of masses m and M are suspended as shown above by strings of negligible mass. If a person holding the upper string lowers the blocks so that they have a constant downward acceleration a, the tension in the string at point P is
M(g−a)
The toy car shown in the figure above enters the vertical circular loop with an initial velocity and moves completely around the loop without friction. If the car has no means of self-propulsion, which of the following is true of the car's acceleration at the instant it is at point P ?
It has components both downward and toward the center of the circle.
An object 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 M2is 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, and M2
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.
The stacks of boxes shown in the figure above are inside an elevator that is moving upward. The masses of the boxes are given in terms of the mass M of the lightest box. How does the magnitude of the force exerted by the top box on the bottom box compare with the magnitude of the force exerted by the bottom box on the top box for each of the stacks?
The two magnitudes are always equal in each of the stacks.
A 5kg object is released from rest near the surface of a planet. The object's vertical position as a function of time is shown in the graph. Which of the following procedures can be used to determine the strength of the gravitational field on the planet?
Use y=y0+vy0t+12ayt2. Use 10s for t, 0 ms for vy0, 400m for y0, and 0m for y. Solve for ay.
A ball of mass m is attached to a vertical rod by two massless strings. The rod is rotated about its axis so that both strings are taut, with tensions T1 and T2, respectively. The strings and rod form the right triangle shown in the figure above. The ball rotates in a horizontal circle of radius rwith speed v. What is the magnitude of the net force on the ball?
mv^2 / r
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.
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
An artificial satellite orbits Earth at a speed of 7800 m/s and a height of 200 km above Earth's surface. The satellite experiences an acceleration due to gravity of
less than 9.8 but greater than 0
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?
0.72N
A 100 kg cart goes around the inside of a vertical loop of a roller coaster. The radius of the loop is 3 m and the cart moves at a speed of 6 m/s at the top. The force exerted by the track on the cart at the top of the loop is
200
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 Rfrom 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 μSbetween the block and the disk?
Determine the slope of the best fit line and set it equal to μSg.
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. Students take measurements of the force F0 , directed to the left, needed to hold the cart in place as well as the tension FT in the horizontal section of string. The students take three measurements for each force. Which of the following sets of measurements would provide the most precise determination of the correct relationship between the net force and the vector sum of the individual forces exerted on the cart?
4.0,4.7, 4.8 & 4.02, 4.65, 4.77
A person is running on a track. Which of the following forces propels the runner forward?
The force of friction exerted by the ground on the person
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 .
A student stands at one end of a raft floating in a pool with equally spaced marks along the bottom, as shown above. The student and the raft have the same mass. The student walks to the opposite end of the raft. Which of the following best shows the final locations of the raft and student relative to the marks at the bottom of the pool? Assume that there is no drag force between the raft and the water.
float moved to the left but not the furthest left
A box of mass m hangs from massless strings, as shown in the figure above. The angle between strings 1 and 2 is 90o, and the angles that the strings make with the ceiling are Ѳ1 and Ѳ2, respectively. If T1 is the tension in string 1, which of the following are the magnitudes of the horizontal and vertical components of the tension in string 2 ?
horizontal: Tcostheta vertical: mg-Tsintheta
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