Circular Motion

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

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

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?

5m/ s^2

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 tanθ

An astronaut performs an experiment near the surface of a moon by releasing an object at rest above a motion detector such that data can be collected about the object's vertical velocity as a function of time. The data are provided in the table. Which of the following graphs most likely represents the shape of the curve of the magnitude of the gravitational field strength near the surface of the moon as a function of time?

horizontal line well above the x-axis option b

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 ?

---------->Fnormal I I I fgravity There is a normal force exerted to the right by the loop, and a gravitational force exerted downward by Earth.

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?

Fg=G Me Ma/ (RE+H)^2

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 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.

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?

Location: Top of circle Acceleration: 3g

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

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?

T=2π √R^3/ GM

A block of known mass M is on a disk that rotates about its center, as shown above. The block does not slip on the disk, and travels at a constant tangential speed v when at a distance R from the center with a centripetal force of magnitude F exerted on it. Which of the following statements about other quantities that might be determined is correct?

The centripetal acceleration of the block can be determined, since ac=v2rac=v2r since the block's tangential speed is known and the radius is known. The coefficient of friction between the block and the disk can be determined, since friction provides the centripetal force and the equation F=μmgF=μmg can be applied.

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 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=mv2rWhen 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.

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

On the surface of Planet X, a 2 kg object is thrown upward with a speed of 20 ms. The object's vertical velocity as a function of time is shown in the graph. Which of the following free-body diagrams represents the gravitational force exerted on the object while it is in free fall?

Fgravity= 8n option 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.

The object's mass The diameter of the circular path

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?

a goes up exponentially over time option B

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?

arrow pointing up left northwest and arrow pointing down