Q: A 3.0 g sample is spun in an ultracentrifuge with a centripetal acceleration of $$250,000g. $$What is the apparent weight of the sample?

$$w_{app} = 250,000 \times (0.0030\,\text{kg}) \times 9.8\,\text{m/s}^2$$

Question 1

A car is rounding a curve of radius $$r at a $$constant speed $$v on a $$level road. What provides the necessary centripetal force for the car to turn?

Accepted Answer

The static friction force between the tires and the road

Question 2

A ball of mass $$m is $$attached to a string and swung in a horizontal circle of radius $$r at $$constant speed $$v. $$What is the magnitude of the tension in the string?

Accepted Answer

$$T = \frac{mv^2$}{r}$$

Question 3

A roller coaster car of mass $$m$$ moves with speed $$v at $$the bottom of a vertical circular loop of radius $$r. $$What is the normal force $$n$$ exerted by the track on the car at this point?

Accepted Answer

$$n = mg + \frac{mv^2$}{r}$$

Question 4

A satellite orbits the Earth in a circular orbit of radius $$r$$ with speed $$v. $$Which equation correctly relates the gravitational force to the required centripetal force?

Accepted Answer

$$\frac{mv^2$}{r} = \frac{GMm}{r^2$}$$

Question 5

If the radius of a planet doubles but its mass remains the same, what happens to the free-fall acceleration $$g at $$its surface?

Accepted Answer

It becomes one-fourth as large

Question 6

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

Frictional force

Question 7

A 1500 kg car turns a corner of radius 20 m on a dry road ($$\mu_s = 1.0). $$What is the maximum speed at which the car can make the turn without sliding?

Accepted Answer

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

Question 8

A satellite is moved from a low Earth orbit to a higher orbit. Which of the following quantities increases?

Accepted Answer

Its orbital period

Question 9

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

Accepted Answer

It moves in a straight line tangent to the exit point

Question 10

The gravitational force between two objects of mass $$m_1$$ and $$m_2$$ separated by distance $$r is $$given by:

Accepted Answer

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

Question 11

A 3.0 g sample is spun in an ultracentrifuge with a centripetal acceleration of $$250,000g. $$What is the apparent weight of the sample?

Accepted Answer

$$w_{app} = 250,000 	imes (0.0030\,	ext{kg}) 	imes 9.8\,	ext{m/s}^2$$

Question 12

A satellite of mass $$m$$ orbits a planet of mass $$M at $$radius $$r. $$What is the speed required for a stable circular orbit?

Accepted Answer

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

Question 13

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

Accepted Answer

It becomes one-fourth as large

Question 14

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

Accepted Answer

$$v_{min} = \sqrt{g r}$$

Question 15

A geostationary satellite orbits the Earth with a period of 24 hours. What is the relationship between the orbital radius $$r$$ and the period $$T$$ for a satellite orbiting a planet of mass $$M$$?

Accepted Answer

$$T^2$$ = \frac{4\$$pi^2$$}{GM} $$r^3$$

Question 16

Why do astronauts in the International Space Station feel weightless?

Accepted Answer

Because they are in free fall

Question 17

A planet has twice the mass and twice the radius of Earth. If the free-fall acceleration at Earth's surface is $$g$$, what is the free-fall acceleration at the surface of this planet?

Accepted Answer

$$\frac{g}{2}$$

Question 18

A coin is rotating on a turntable and the frictional force suddenly disappears. What path does the coin follow?

Accepted Answer

It moves in a straight line tangent to the circle

Question 19

Which of the following statements about centripetal acceleration is correct for an object in uniform circular motion?

Accepted Answer

It is always directed toward the center of the circle

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

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