Q: A satellite orbits the Earth at a height where the acceleration due to gravity is $$8.7\ \mathrm{m/s^2$}. If $$the radius of the Earth is $$6.37 \times 10^6$\ \mathrm{m}$$, what is the distance from the center of the Earth to the satellite?

$$7.45 \times 10^6$\ \mathrm{m}$$

Q: A highway curve is banked at an angle $$ heta so $$that a car can safely negotiate the curve at speed $$v$$ without relying on friction. Which equation relates the banking angle to the speed $$v$$, radius $$r$$, and gravitational acceleration $$g$$?

$$\tan \theta = \dfrac{v^2$}{g r}$$

Question 1

A ball of mass $$0.150\ \mathrm{kg} is $$attached to a string and revolves uniformly in a horizontal circle of radius $$0.60\ \mathrm{m}$$, making $$2.00$$ revolutions per second. What is the magnitude of the centripetal acceleration of the ball?

Accepted Answer

$$9.47\ \mathrm{m/s^2$}$$

Question 2

Which of the following best describes the direction of the acceleration vector for an object in uniform circular motion?

Accepted Answer

Perpendicular to the velocity and directed toward the center of the circle

Question 3

A car travels around a flat, unbanked curve of radius $$50\ \mathrm{m} at a $$constant speed of $$20\ \mathrm{m/s}. $$What is the minimum coefficient of static friction required between the tires and the road to prevent the car from skidding?

Accepted Answer

$$0.41$$

Question 4

Which of the following statements about centripetal force is correct?

Accepted Answer

It is the net force directed toward the center of the circle, provided by other physical forces.

Question 5

A satellite orbits the Earth at a height where the acceleration due to gravity is $$8.7\ \mathrm{m/s^2$}. If $$the radius of the Earth is $$6.37 	imes 10^6$\ \mathrm{m}$$, what is the distance from the center of the Earth to the satellite?

Accepted Answer

$$7.45 	imes 10^6$\ \mathrm{m}$$

Question 6

Which equation gives the magnitude of the centripetal acceleration $$a_c$$ for an object moving at speed $$v in a $$circle of radius $$r$$?

Accepted Answer

$$a_c = \dfrac{v^2$}{r}$$

Question 7

Newton’s law of universal gravitation states that the gravitational force between two masses $$m_1$$ and $$m_2$$ separated by a distance $$r is$$:

Accepted Answer

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

Question 8

A $$2.0\ \mathrm{kg}$$ object is moving in a circle of radius $$0.5\ \mathrm{m} at a $$constant speed of $$4.0\ \mathrm{m/s}. $$What is the magnitude of the net force acting on the object?

Accepted Answer

$$32\ \mathrm{N}$$

Question 9

Which of the following is NOT a consequence of Kepler’s laws of planetary motion?

Accepted Answer

The orbits of planets are perfect circles.

Question 10

A highway curve is banked at an angle $$	heta so $$that a car can safely negotiate the curve at speed $$v$$ without relying on friction. Which equation relates the banking angle to the speed $$v$$, radius $$r$$, and gravitational acceleration $$g$$?

Accepted Answer

$$	an 	heta = \dfrac{v^2$}{g r}$$

Question 11

If the period of revolution for a satellite in circular orbit around Earth is doubled, by what factor does the centripetal acceleration change?

Accepted Answer

It decreases by a factor of $$4$$

Question 12

Which of the following best explains why astronauts in orbit experience 'weightlessness'?

Accepted Answer

They are in continuous free fall toward Earth, accelerating at the same rate as their spacecraft.

Question 13

A $$1.0\ \mathrm{kg}$$ object is swung in a vertical circle of radius $$2.0\ \mathrm{m} at a $$constant speed of $$6.0\ \mathrm{m/s}. $$What is the tension in the string at the bottom of the circle?

Accepted Answer

$$38\ \mathrm{N}$$

Question 14

Which of the following is a correct statement about the gravitational acceleration $$g$$ near Earth's surface?

Accepted Answer

$$g$$ decreases with increasing altitude above Earth's surface.

Question 15

Which of the following is NOT one of the four fundamental forces in nature?

Accepted Answer

Centripetal force

Question 16

A planet orbits the Sun in an elliptical path. According to Kepler’s second law, when is the planet moving fastest?

Accepted Answer

When it is closest to the Sun (perihelion)

Question 17

A $$0.5\ \mathrm{kg}$$ mass is attached to a $$1.0\ \mathrm{m}$$ string and swung in a horizontal circle at $$3.0\ \mathrm{m/s}. $$What is the tension in the string?

Accepted Answer

$$9.0\ \mathrm{N}$$

Question 18

Which of the following best describes the path of a projectile launched horizontally from a high altitude in the absence of air resistance and neglecting Earth's rotation?

Accepted Answer

It follows a curved path due to gravity, eventually striking the ground.

Circular Motion and Gravitation: Kinematics of Uniform Circular Motion

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