Q: A car of mass 1500 kg goes over a hill shaped as a circular arc of radius 60 m at a speed of 20 m/s. What is the normal force exerted by the road on the car at the top of the hill? (Take $$g = 9.8\ \mathrm{m/s^2$}.)$$

$$n = 1500 \times 9.8 - \frac{1500 \times (20)^2$}{60} = 14,700 - 10,000 = 4,700\ \mathrm{N}$$

Q: A 0.0030 kg sample is spun in an ultracentrifuge of radius 0.09 m at a centripetal acceleration of $$250,000g. $$What is the apparent weight of the sample? ($$g = 9.8\ \mathrm{m/s^2$})$$

$$0.0030 \times 250,000 \times 9.8 = 7,350\ \mathrm{N}$$

Q: A 7.3 kg hammer is swung in a horizontal circle of radius 1.2 m at a speed of 29 m/s. What is the tension in the chain?

$$T = \frac{7.3 \times (29)^2$}{1.2} = 5,110\ \mathrm{N}$$

Q: A 65 kg student sits 0.60 m from another 65 kg student. What is the magnitude of the gravitational force between them? ($$G = 6.67 \times 10$$^{-11}$$\ \mathrm{N\,m^2$/kg^2$$}$)

$$F = 6.67 \times 10$$^{-11}$$ \times \frac{65 \times 65}{0.60^2$} = 7.8 \times 10$$^{-8}$$\ \mathrm{N}$$

Question 1

A car of mass 1500 kg goes over a hill shaped as a circular arc of radius 60 m at a speed of 20 m/s. What is the normal force exerted by the road on the car at the top of the hill? (Take $$g = 9.8\ \mathrm{m/s^2$}.)$$

Accepted Answer

$$n = 1500 	imes 9.8 - \frac{1500 	imes (20)^2$}{60} = 14,700 - 10,000 = 4,700\ \mathrm{N}$$

Question 2

Which force provides the centripetal acceleration for a car turning a corner on a level (unbanked) road?

Accepted Answer

Friction

Question 3

A 0.0030 kg sample is spun in an ultracentrifuge of radius 0.09 m at a centripetal acceleration of $$250,000g. $$What is the apparent weight of the sample? ($$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$0.0030 	imes 250,000 	imes 9.8 = 7,350\ \mathrm{N}$$

Question 4

A satellite orbits Earth in a circular orbit of radius $$r. $$What is the speed required to maintain this orbit? (Earth's mass is $$M.)$$

Accepted Answer

$$v = \sqrt{\frac{GM}{r}}$$

Question 5

If the distance between two masses is doubled, what happens to the gravitational force between them?

Accepted Answer

It is quartered

Question 6

A 7.3 kg hammer is swung in a horizontal circle of radius 1.2 m at a speed of 29 m/s. What is the tension in the chain?

Accepted Answer

$$T = \frac{7.3 	imes (29)^2$}{1.2} = 5,110\ \mathrm{N}$$

Question 7

A roller coaster car of mass $$m$$ moves at speed $$v at $$the top of a vertical loop of radius $$r. $$What is the minimum speed required at the top so that the car stays on the track?

Accepted Answer

$$v = \sqrt{g r}$$

Question 8

A 60 kg person stands on two different planets. On which planet is her weight the greatest?

Accepted Answer

On the planet with the largest mass and smallest radius

Question 9

A coin sits on a turntable rotating at constant speed. What force acts in the plane of the turntable to keep the coin moving in a circle?

Accepted Answer

Friction

Question 10

A car of mass $$m$$ turns a corner of radius $$r on a $$flat road. If the coefficient of static friction is $$\mu_s$$, what is the maximum speed before the car starts to skid?

Accepted Answer

$$v_{max} = \sqrt{\mu_s g r}$$

Question 11

A satellite is boosted into a higher circular orbit around Earth. Which of the following quantities increases?

Accepted Answer

Period

Question 12

What is the direction of the acceleration for an object in uniform circular motion?

Accepted Answer

Toward the center of the circle

Question 13

A ball is swung in a horizontal circle at constant speed. What is the direction of the net force on the ball?

Accepted Answer

Toward the center of the circle

Question 14

The International Space Station orbits Earth about 15 times per day. Why do astronauts inside feel weightless?

Accepted Answer

They are in free fall

Question 15

Two identical satellites have different circular orbits around Earth. Which one has the higher speed?

Accepted Answer

The one in the smaller orbit

Question 16

A 65 kg student sits 0.60 m from another 65 kg student. What is the magnitude of the gravitational force between them? ($$G = 6.67 	imes 10$$^{-11}$$\ \mathrm{N\,m^2$/kg^2$$}$)

Accepted Answer

$$F = 6.67 	imes 10$$^{-11}$$ 	imes \frac{65 	imes 65}{0.60^2$} = 7.8 	imes 10$$^{-8}$$\ \mathrm{N}$$

Question 17

A ball is shot through a hollow tube lying flat on a table and emerges from the other end. What path does it follow after leaving the tube?

Accepted Answer

It continues in a straight line tangent to the circle at the exit point

Question 18

If the mass of one object is doubled and the distance between two objects is also doubled, what happens to the gravitational force between them?

Accepted Answer

It is halved

Question 19

A car is moving at constant speed through a dip in the road shaped as a circular arc. At the bottom of the dip, how does the normal force compare to the car's weight?

Accepted Answer

Normal force is greater than the weight

Question 20

Which of the following best describes Newton's law of universal gravitation?

Accepted Answer

The force is directly proportional to the product of the masses and inversely proportional to the square of the distance between them

Chapter 6: Circular Motion, Orbits, and Gravity – Study Notes

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