A ball is fastened to a string and is swung in a vertical circle. When the ball is at the highest point of the circle its velocity and acceleration directions are:

(B) (C) (D)

A ball with a mass m is fastened to a string and is swung in a vertical circle. When the ball is at the lowest point of the circle the tension in the string is:

mg (B) mg + ma (C) ma -mg (D) mg/ma

A child whirls a ball at the end of a rope, in a uniform circular motion. Which of the following statements is NOT true?

The speed of the ball is constant.

The velocity of the ball is constant.

The radius is constant

The magnitude of the ball’s acceleration is constant.

A small sphere is moving in a vertical circle of a constant radius at constant speed. The magnitude of the net force on the sphere

at the bottom of the loop is greater than the net force at the top.

at the top of the loop is greater than the net force at the bottom.

decreases as the sphere moves from the bottom to the top.

is the same at the top of the loop as it is at the bottom of the loop.

An object moves in a circular path at a constant speed. Compare the direction of the object’s velocity and acceleration vectors.

The vectors point in opposite directions.

The vectors are perpendicular.

The vectors form some acute angle.

The question is meaningless, since the acceleration is zero.

A roller coaster car is on a track that forms a circular loop in the vertical plane. If the car is to just maintain contact with track at the top of the loop, what is the minimum value for its centripetal acceleration at this point?

g downward

g upward

2g upward

2g downward

A pilot executes a vertical dive then follows a semi-circular arc until it is going straight up. Just as the plane is at its lowest point, the force of the seat on him is

less than mg, and pointing down.

more than mg, and pointing up.

more than mg, and pointing down.

the same as mg.

A ball attached to a string is whirled around in a horizontal circle having radius r. If the radius of the circle is changed to r/4 and the same centripetal force is applied by the string, the new speed of the ball is which of the following.

One-quarter of the original speed

One-half of the original speed

Twice the original speed

Four times the original speed

A penny is resting on a turntable. What is the force responsible for keeping the penny from sliding off?

Normal force

Gravitational force

Frictional force

There is no force.

Is it possible for an object moving with a constant speed to accelerate? Explain.

No, if the speed is constant then the acceleration is equal to zero.

No, an object can accelerate only if there is a net force acting on it.

Yes, although the speed is constant, the direction of the velocity can be changing.

Yes, if an object is moving it can experience acceleration.

Multi-Correct Questions 11-14

Directions: For each of the following, two of the suggested answers will be correct. Select the best two choices to earn credit. No partial credit will be earned if only one correct choice is selected.

An object at the end of a string is used as a conical pendulum. Which of the following would you need to know in order to calculate the tension in the string?

The angle

The mass of the string

The mass of the object

The frequency of its motion

Four particles have the following masses (in terms of m), speeds (in terms of v), and radii (in terms of r). Which two particles have the same centripetal force?

Particle Mass Speed Radius

1 m v r

2 m/4 2v r

3 2m v/2 r

4 3m 2v 3r

Particle 1

Particle 2

Particle 3

Particle 4

A satellite of mass m moves in a circular orbit of radius R around a planet of mass M with speed v. Which of these must be true for the satellite?

The net force on it is MR/v2

Its acceleration is GM/R

Its orbital velocity is (GM/R)1/2

Its orbital period is 2pR/v

Based on the masses and radii of the following planets, which two will have the same surface gravity?

Planet A with a mass of M and a radius of R.

Planet B with a mass of 2M and a radius of 2R.

Planet C with a mass of M and a radius of 2R.

Planet D with a mass of 4M and a radius of 2R.

A hypothetical planet orbits a star with mass 4 times the mass of our sun. The planet’s orbital radius is the same as the Earth’s. Approximately how many Earth years does it take for the planet to complete one orbit?

1/2 (B)1/v2 (C) 1 (D) v2

As a rocket moves away from the Earth’s surface, the rocket’s weight

(A)increases. (B)decreases. (C)remains the same.

(D)depends on how fast it is moving.

Two artificial satellites, 1 and 2, are put into circular orbit at the same altitude above Earth’s surface. The mass of satellite 2 is half the mass of satellite 1. If the period of satellite 1 is T, what is the period of satellite 2?

T/2 (B) T (C) 2T (D) 4T

A satellite encircles Mars at a distance above its surface equal to 3 times the radius of Mars. The acceleration of gravity of the satellite, as compared to the acceleration of gravity on the surface of Mars, is

(A)zero. (B)the same. (C)one-ninth as much. (D)one-sixteenth as much.

A planet has a radius twice that of Earth and a ten times the Earth’s mass. The gravitational acceleration at the surface of the planet is most nearly

(A) 4.0 m/s2 (B) 8.0 m/s2 (C) 12.5 m/s2 (D) 25 m/s2

In the following problem, the word “weight” refers to the force a scale registers. If the Earth were to increase its rotating speed, but not change shape,

the weight of an object at the equator would increase.

the weight of an object at the equator would decrease.

the weight of an object at the North Pole would increase.

the weight of an object at the North Pole would decrease.

The radius of Earth is R. At what distance above Earth’s surface will the acceleration of gravity be 2.45 m/s2?

(A) 0.41 R (B) 1.0 R (C) 1.41 R (D) 2R

What happens to the force of gravitational attraction between two small objects if the distance between their centers is halved?

(A) It is doubled (B) It is quadrupled (C) It is halved (D) It is reduced fourfold

Two planets have the same surface gravity, but planet B has twice the mass of planet A. If planet A has radius r, what is the radius of planet B?

0.707r

r

1.41r

4r

Two spheres, with radii of R, are in contact with each other and attract each other with a force of F. If the radii of both of the spheres are cut to half while the density remains the same, what is the new gravitational force between them?

(A) 16F (B) 4F (C)F/2 (D) F/16

After firing a cannon ball, the cannon moves in the opposite direction from the ball. This an example of:

A. Newton’s First Law

B. Newton’s Second Law

C. Newton’s Third Law

D. Newton’s Law of Gravitation

E. None of the above

A heavy box sits on a floor. The net force on the box can be represented as which of the following?

A. Non-zero vector pointing up

B. Non-zero vector pointing down

C. Non-zero vector pointing left

D. Non-zero vector pointing right

E. It is zero

A box that weighs 25 N is pulled by an applied force of 10 N. The coefficient of static friction between the box and the surface is 0.5. The box will:

A. start moving and will continue to increase its velocity

B. start moving and maintain a constant velocity

C. start moving and continue to increase its acceleration

D. not move

E. start moving and then slow to a stop

In the diagram to the right, two blocks A and B with masses m and 2m are in contact on a horizontal frictionless surface. A force F is applied to block A. Use this diagram to answer questions 39 and 40.

What is the acceleration of the system of two blocks?

A. F/m

B. F/2m

C. F/3m

D. F/4m

E. F/5m

What is the force exerted by block A on block B?

A. F/2

B. F/3

C. 3F/2

D. 2F/3

E. F/5

The answer is C

1. Two blocks with masses m1 and m2, respectively, are connected by a light string, as shown below. Block 1 is placed on an inclined plane which makes an angle ? with the horizontal. Block 2 is suspended from a pulley that is attached to the top on the inclined plane. The coefficient of kinetic friction between block 1 and the incline is µk.

Block 1 moves up the inclined plane with a constant velocity v. On the diagram below show all the applied forces on each block.

Determine the mass of block 2 that allows block 1 to move up the incline with a constant speed.

Determine the mass of block 2 that will cause block 1 to accelerate up the incline at a constant rate a.

The string between the blocks is cut. Determine the acceleration of block 1.

A shuttle of mass m is in a circular orbit at a height h above the surface of the Earth, which has mass Me and radius Re. Express your answers in terms of h, m, Me, Re, and G.

On the diagram above, draw and label the velocity and acceleration vectors of the shuttle at point P.

Write the equation that can describe the gravitational force on the shuttle.

Derive the equation for the shuttle’s acceleration when it is in orbit

Derive the equation for the velocity of the satellite as it stays in orbit.

How will the velocity change if the shuttle increases its height above the surface? Explain.

If the shuttle’s period is synchronized with that of Earth’s rotation, what is the height of the shuttle? (1 day = 8.64x104s, ME = 6x1024kg, RE = 6.4x106m)

A ball of mass M attached to a string of length L moves at constant speed v in a circle in a vertical plane as shown above. At the bottom, the ball just clears the ground. Air resistance is negligible. Express all answers in terms of M, L, v, and g.

Draw and label all forces acting on the ball when it is at the top of the circle.

Determine the magnitude and direction of the tension force on the ball when it is at the top.

Draw and label all forces acting on the ball when it is at the bottom of the circle.

Determine the magnitude and direction of the tension force on the ball when it is at the bottom.

The string is then cut when the ball is at the top.

Determine the time it takes the ball to reach the ground.

Determine the horizontal distance the ball travels before hitting the ground.

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