Q: A 1,000-kg car rounds a banked curve of radius $$100\ \mathrm{m} at a $$speed of $$20\ \mathrm{m/s}. If $$the curve is banked at the correct angle for this speed, what is the angle of the bank (neglect friction)?

$$\theta = \arctan\left(\frac{v^2$}{rg}\right)$$, so $$\theta \approx 22.5^\circ$$

Question 1

A ball of mass $$0.150\ \mathrm{kg} is $$attached to a string and revolves uniformly in a horizontal circle of radius $$0.600\ \mathrm{m}$$, making $$2.00$$ revolutions per second. What is the magnitude of its centripetal acceleration?

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

It is always 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. If the coefficient of static friction between the tires and the road is $$0.40$$, what is the maximum speed the car can have without skidding?

Accepted Answer

$$14\ \mathrm{m/s}$$

Question 4

Which of the following statements about centripetal force is correct?

Accepted Answer

Centripetal force is not a new kind of force, but the name given to the net force causing circular motion.

Question 5

A satellite orbits the Earth in a circular orbit of radius $$r. If $$the radius of the orbit is doubled, how does the satellite's speed change?

Accepted Answer

It decreases by a factor of $$1/\sqrt{2}.$$

Question 6

According to Newton's law of universal gravitation, the gravitational force between two masses $$m_1$$ and $$m_2$$ separated by a distance $$r is $$given by:

Accepted Answer

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

Question 7

A 70-kg astronaut weighs less on the Moon than on Earth because:

Accepted Answer

The acceleration due to gravity on the Moon is less than on Earth.

Question 8

Which of the following is NOT a correct statement about Kepler's laws of planetary motion?

Accepted Answer

All planets move in perfect circles around the Sun.

Question 9

A 1,000-kg car rounds a banked curve of radius $$100\ \mathrm{m} at a $$speed of $$20\ \mathrm{m/s}. If $$the curve is banked at the correct angle for this speed, what is the angle of the bank (neglect friction)?

Accepted Answer

$$	heta = \arctan\left(\frac{v^2$}{rg}ight)$$, so $$	heta \approx 22.5^\circ$$

Question 10

If the period of revolution for a particle in uniform circular motion is $$T$$, what is the frequency $$f$$?

Accepted Answer

$$f = \frac{1}{T}$$

Question 11

A geostationary satellite orbits the Earth once every 24 hours. What is true about its position relative to the Earth's surface?

Accepted Answer

It remains above the same point on the equator at all times.

Question 12

Which of the following is a correct expression for the centripetal acceleration $$a_c of an $$object moving at speed $$v in a $$circle of radius $$r$$?

Accepted Answer

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

Question 13

A person standing on a scale in an elevator notices that the scale reads less than their normal weight. Which of the following best explains this observation?

Accepted Answer

The elevator is accelerating downward.

Question 14

Which of the following is NOT a fundamental force of nature?

Accepted Answer

Frictional force

Question 15

A 0.5-kg mass is swung in a vertical circle of radius $$1.0\ \mathrm{m} at a $$constant speed of $$4.0\ \mathrm{m/s}. $$What is the tension in the string at the top of the circle?

Accepted Answer

$$6.9\ \mathrm{N}$$

Question 16

If the Moon's mass were doubled but its orbital radius remained the same, how would the gravitational force between the Earth and the Moon change?

Accepted Answer

It would double.

Question 17

Which of the following best explains why astronauts in orbit feel 'weightless'?

Accepted Answer

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

Question 18

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

Accepted Answer

When it is closest to the Sun (perihelion).

Question 19

A 2-kg object moves in a circle of radius $$0.5\ \mathrm{m} at a $$constant speed of $$3\ \mathrm{m/s}. $$What is the net force acting on the object?

Accepted Answer

$$36\ \mathrm{N}$$

Circular Motion and Gravitation: Concepts and Applications

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