Q: A 5 kg mass is placed 2 m away from a 10 kg mass. What is the magnitude of the gravitational force between them? (Use $$G = 6.67 \times 10$$^{-11}$$ \ \mathrm{N \cdot m^2$ / kg^2$})$$

$$F = 1.67 \times 10$$^{-10}$$ \ \mathrm{N}$$

Question 1

A car of mass $$m$$ travels at a constant speed $$v$$ around a flat circular track of radius $$r. $$What is the magnitude of the centripetal force required to keep the car moving in a circle?

Accepted Answer

$$F = m v^2$ / r$$

Question 2

Which of the following best describes the direction of the centripetal force acting on an object moving in a circular path?

Accepted Answer

It is directed toward the center of the circle.

Question 3

A satellite orbits the Earth in a circular orbit. Which force provides the necessary centripetal force for its motion?

Accepted Answer

The gravitational force between the Earth and the satellite.

Question 4

According to Newton's Law of Universal Gravitation, what happens to the gravitational force between two masses if the distance between them is doubled?

Accepted Answer

The force becomes one-fourth as large.

Question 5

Which of the following equations correctly represents Newton's Law of Universal Gravitation?

Accepted Answer

$$F = G \frac{m_1$ m_2$}{r^2$}$$

Question 6

A 2 kg object is attached to a string and swung in a horizontal circle of radius 1.5 m at a speed of 3 m/s. What is the tension in the string?

Accepted Answer

$$T = 12 N$$

Question 7

If the mass of the Earth were doubled, but its radius remained the same, how would the gravitational acceleration at the surface change?

Accepted Answer

It would double.

Question 8

A person in a car going around a sharp curve feels as if they are being pushed outward. What is the best explanation for this sensation?

Accepted Answer

It is due to inertia; the person wants to continue in a straight line while the car turns.

Question 9

Which of the following statements about centrifugal force is correct?

Accepted Answer

It is a fictitious force that appears in a rotating reference frame.

Question 10

A geostationary satellite orbits the Earth at a fixed position above the equator. Which of the following must be true about its orbital period?

Accepted Answer

It must be equal to the rotational period of the Earth (24 hours).

Question 11

A 5 kg mass is placed 2 m away from a 10 kg mass. What is the magnitude of the gravitational force between them? (Use $$G = 6.67 	imes 10$$^{-11}$$ \ \mathrm{N \cdot m^2$ / kg^2$})$$

Accepted Answer

$$F = 1.67 	imes 10$$^{-10}$$ \ \mathrm{N}$$

Question 12

Which of the following best explains why astronauts in the International Space Station appear weightless?

Accepted Answer

They are in continuous free fall around the Earth.

Question 13

A 1,000 kg car takes a turn of radius 50 m at a speed of 20 m/s. What is the minimum frictional force required to prevent the car from skidding?

Accepted Answer

$$F = 8,000 N$$

Question 14

If the radius of a planet is tripled but its mass remains the same, how does the gravitational acceleration at its surface change?

Accepted Answer

It becomes one-ninth as large.

Question 15

A ball is swung in a vertical circle at constant speed. At the top of the circle, which forces act on the ball?

Accepted Answer

Both gravity and the tension in the string act downward.

Question 16

Which of the following is a correct statement about the relationship between centripetal acceleration and velocity?

Accepted Answer

$$a_c = v^2$ / r$$

Question 17

A 70 kg astronaut stands on the surface of Mars, which has a mass of $$6.4 	imes 10$$^{23}$$ kg and a radius of 3.4$$ 	imes $$10^6 m. $$What is the gravitational force acting on the astronaut? (Use $$G = 6.67 	imes 10$$^{-11}$$ \ \mathrm{N \cdot m^2$ / kg^2$})$$

Accepted Answer

$$F \approx 250 N$$

Question 18

Which of the following is NOT a property of gravitational force according to Newton's Law of Gravity?

Accepted Answer

It acts only on objects with electric charge.

Question 19

A roller coaster car of mass $$m$$ goes over the top of a hill of radius $$r at $$speed $$v. $$What is the normal force exerted by the track on the car at the top of the hill?

Accepted Answer

$$N = m g - m v^2$ / r$$

Question 20

Which of the following real-world scenarios best illustrates the concept of centripetal force?

Accepted Answer

A child being pushed toward the center while spinning on a merry-go-round.

Centripetal and Centrifugal Forces, and Newton’s Law of Gravity

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