Q: A car is negotiating a banked curve of radius $$r at a $$speed $$v$$ without relying on friction. Which of the following equations correctly relates the banking angle $$\theta to $$the speed $$v$$, radius $$r$$, and gravitational acceleration $$g$$?

$$\tan \theta = \frac{v^2$}{rg}$$

Q: A cyclist rounds a banked curve of radius 30 m at a speed of 15 m/s. What is the ideal banking angle $$\theta ($$neglecting friction)? (Use $$g = 9.8\ \mathrm{m/s^2$})$$

$$\tan \theta = \frac{225}{294} \approx 0.77$$

Question 1

A car is negotiating a banked curve of radius $$r at a $$speed $$v$$ without relying on friction. Which of the following equations correctly relates the banking angle $$	heta to $$the speed $$v$$, radius $$r$$, and gravitational acceleration $$g$$?

Accepted Answer

$$	an 	heta = \frac{v^2$}{rg}$$

Question 2

A 1 kg mass is placed 1 meter above Earth's surface. What is the gravitational force acting on it due to Earth? (Use $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$9.8\ \mathrm{N}$$

Question 3

Which of the following best explains why astronauts experience weightlessness while orbiting the Earth in the International Space Station?

Accepted Answer

They are in continuous free fall around the Earth, so the normal force is zero.

Question 4

A satellite orbits the Earth at a distance $$r$$ from the center of the Earth. Which formula gives the gravitational force acting on the satellite of mass $$m$$? (Earth's mass is $$M$$ and $$G is $$the gravitational constant.)

Accepted Answer

$$F = \frac{G M m}{r^2$}$$

Question 5

A 2 kg object moves in a circle of radius 4 m at a constant speed of 6 m/s. What is the magnitude of the centripetal force acting on it?

Accepted Answer

$$18\ \mathrm{N}$$

Question 6

Which of the following statements about the Moon's orbit around the Earth is correct?

Accepted Answer

The gravitational force from the Earth provides the centripetal force for the Moon's orbit.

Question 7

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

Accepted Answer

It becomes one-fourth as large.

Question 8

A car travels around a flat curve of radius $$r at $$speed $$v. $$What provides the necessary centripetal force for the car to turn?

Accepted Answer

Friction between the tires and the road.

Question 9

A 70 kg astronaut in orbit experiences muscle atrophy and bone mass loss. What is the primary cause of these physiological changes?

Accepted Answer

Prolonged exposure to weightlessness reduces the mechanical load on muscles and bones.

Question 10

A ball is swung in a horizontal circle at the end of a string. If the speed of the ball is doubled, how does the required centripetal force change?

Accepted Answer

It increases by a factor of 4.

Question 11

Which of the following best describes the direction of the centripetal acceleration for an object moving in a circle?

Accepted Answer

It is always directed toward the center of the circle.

Question 12

A marble, a ball, and a spoon are dropped from the same height in a vacuum. Which will hit the ground first?

Accepted Answer

They all hit the ground at the same time.

Question 13

A car is moving at 20 m/s around a curve of radius 50 m. What is the required centripetal acceleration?

Accepted Answer

$$8\ \mathrm{m/s^2$}$$

Question 14

Which of the following is a correct expression for centripetal acceleration $$a_c$$?

Accepted Answer

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

Question 15

If the gravitational force between two objects is $$F$$, what will the force be if the distance between them is tripled?

Accepted Answer

$$\frac{F}{9}$$

Question 16

A cyclist rounds a banked curve of radius 30 m at a speed of 15 m/s. What is the ideal banking angle $$	heta ($$neglecting friction)? (Use $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$	an 	heta = \frac{225}{294} \approx 0.77$$

Question 17

Which of the following is NOT a consequence of long-term microgravity exposure?

Accepted Answer

Increased bone density

Question 18

A tennis player swings a racquet in a circle of radius 1 m at a tip speed of 20 m/s. What is the centripetal acceleration at the tip?

Accepted Answer

$$400\ \mathrm{m/s^2$}$$

Question 19

Which of the following best describes the role of friction in a car negotiating a flat (unbanked) curve?

Accepted Answer

Friction provides the centripetal force required to keep the car moving in a circle.

Question 20

If the mass of one object is doubled and the distance between two objects is halved, how does the gravitational force between them change?

Accepted Answer

It increases by a factor of 8.

Chapter 6: Gravitational Forces, Centripetal Motion, and Microgravity: Study Notes

Study Guide - Practice Questions

Study Guide - Flashcards