Circular Motion and Gravitation

Question 1

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

A. Both vectors point in the same direction.

B. The vectors point in opposite directions.

C. The vectors are perpendicular.

D. The question is meaningless, since the 
​acceleration is zero.

Answer 1

C

Question 2

A ball is held on a string and is moving in a circular motion, the radius of the circle is 4cm and the time it takes for the ball to make a full turn is 7 seconds, the ball moves at an average speed of

A. 3.6 cm/s
B. 6.1 cm/s
C. 7.7 cm/s
D. 3.6 m/s

Answer 2

(A)
2πr ÷ time
2π4 ÷ 7

Question 3

A student on an amusement park ride moves in a circular path with a radius of 3.5 meters once every 8.9 seconds the students moves at an average speed of:

A. 4.2 m/s
B. 2.5 m/s
C. 0.81 m/s
D. 7.3 m/s

Answer 3

(B)
2πr ÷ time
2π4 ÷ 7

Question 4

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

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

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

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

D. Yes, if an object is moving it is experiencing 
​acceleration

Answer 4

C

Question 5

A ball is swung in a circle. The frequency of the ball is doubled. By what factor does the period change

A. It doubles

B. It quadruples

C. It doesn’t change

D. it is halved

Answer 5

(D)

Since frequency is the inverse of the period it is halved

Question 6

Two cars go around the same circular track at the same speed. The first car is closer to the inside of the circle. Which of the following is true about their centripetal acceleration?

A. Both cars have the same centripetal motion since they both have the same speed.

B. The centripetal acceleration of the second car is greater since its radius is larger.

C. The centripetal acceleration of the first car is greater since its radius is smaller.

Answer 6

(C)

Question 7

When an object experiences uniform circular 
​motion, the direction of the net force is:

A. is directed toward the center of the circular path.

B. in the same direction as the motion of the object.

C. is directed away from the center of the circular ​path.

D. away from the string

Answer 7

(A)

Question 8

The model airplane has a mass of 0.90kg and moves at constant speed on a circle that is parallel to the ground. The path of the airplane and the guideline lie in the same horizontal plane because the weight of the plane is balanced by the lift generated by its wings. Find the tension in the 17m guideline for a speed of 19 m/s.

A. 19N

B. 85N

C. 213N

Answer 8

Tension = M x V^2/r

Tension = 0.90kg x 19m/s^2/ 17m

Tension = 19N

Question 9

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?

A. g upward

B. 0.5g downward

C. g downward

D. 2g upward

Answer 9

(C)

Question 10

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:

A. less than mg and pointing up.

B. more than mg and pointing up

C. less than mg and pointing down.

D. more than mg and pointing up.

Answer 10

(D)

Question 11

What is the magnitude of the gravitational force between Earth and its moon?
r = 3.8 x 108m
mEarth = 6.0 x 1024kg
mMoon = 7.3 x 1022 kg

A 2.0 x 10 18 N
B. 2.0 x 1019 N
C. 2.0 x 1020 N
D. 2.0 x 1021 N

Answer 11

(C)

Question 12

What is the magnitude of the gravitational force between Earth and its sun?
r = 1.5 x 1011 m
mEarth = 6.0 x 1024kg
mSun = 2.0 x 1030 kg

A 3.6 x 10-18 N
B 3.6 x 1019 N
C 3.6 x 1021 N
D 3.6 x 1022 N

Answer 12

(D)

Question 13

The gravitational force between two objects is F. What is the force F’ between those objects when the distance between them is halved?

A. 1/2 F
B. 1/4 F
C. 2F
D. 4F

Answer 13

(D)

Question 14

Determine the surface gravity of Earth’s moon. Its mass is 7.4 x 1022 kg and its radius is 1.7 x 106 m.

A. 1.7 m/s2

B. 2.9 m/s2

C. 4.4 m/s2

D. 6.2 m/s2

Answer 14

(A)

Question 15

Compute g for the surface of a planet whose radius is double that of the Earth and whose mass is triple that of Earth.

A. 1.89 m/s2

B. 3.36 m/s2

C. 5.91 m/s2

D. 7.32 m/s2

Answer 15

3/4g of earth

Question 16

Compute g for the surface of a planet whose radius is double that of the Earth and whose density is the same as that of Earth.

A. 1/4 g earth
B. 1/2 g earth
C. 2 g earth
D. 4 g earth

Answer 16

(C)

Question 17

Compute g for the surface of a planet whose radius is half that of Earth and whose density is 3/2 that of Earth.

A 1.7 N/kg
B 2.5 N/kg
C 7.4 N/kg
D 13 N/kg

Answer 17

(C)

Question 18

Compute g at a distance of 7.3 x 108 m from the center of a spherical object whose mass is 3.0 x 1027 kg.

A. 0.38 m/s2

B. 0.55 m/s2

C. 0.71 m/s2

D. 0.88 m/s2

Answer 18

(A)

Question 19

Use your previous answer to determine the velocity, both magnitude and direction, for an object orbiting at a distance of 7.3 x 108 m from the center of a spherical object whose mass is 3.0 x 1027 kg.

A 3.1x103 m/s
B 8.8x103 m/s
C 1.6x104 m/s
D 5.5x104 m/s

Answer 19

(C)

Question 20

What is the orbital period (in days) of an unknown object orbiting the sun with an orbital radius of twice that of earth?

A.470 days

B.690 days

C.854 days

D.1032 days

Answer 20

(D)