Q: A 1500 kg car takes a turn around a curve of radius 20 m on a level road. If the coefficient of static friction is 1.0, what is the maximum speed the car can have without sliding?

$$v = \sqrt{\mu_s g r} = \sqrt{1.0 \times 9.8 \times 20} \approx 14\,\text{m/s}$$

Q: A skateboarder attempts a loop-the-loop in a full pipe with a diameter of 4.3 m. What is the minimum speed required at the very top of the loop to avoid falling?

$$v = \sqrt{g r} = \sqrt{9.8 \times 2.15} \approx 4.6\,\text{m/s}$$

Q: Two people, each of mass 65 kg, are seated 0.60 m apart. What is the magnitude of the gravitational force between them? ($$G = 6.67 \times 10$$^{-11}$$\,\text{N}\cdot\text{m}^2/\text{kg}^2)$$

$$F = 7.6 \times 10$$^{-8}$$\,\text{N}$$

Q: A geostationary satellite orbits the Earth so that it appears stationary above the equator. What is the radius of its orbit? (Earth mass $$M_E = 5.98 \times 10$$^{24}$$\,\text{kg}$$, $$G = 6.67 \times 10$$^{-11}$$\,\text{N}\cdot\text{m}^2/\text{kg}^2$$, period $$T = 24$$ hours)

$$r = 4.22 \times 10^7$\,\text{m}$$

Q: A circular blade of a table saw is 0.30 m in diameter and spins at 120 revolutions per second. What is the speed of a tooth at the edge of the blade?

$$v = 2 \pi r f = 2 \pi \times 0.15 \times 120 \approx 113\,\text{m/s}$$

Question 1

A softball pitcher throws a ball in a circular arc at a steady speed. At the instant shown, what is the direction of the ball's acceleration?

Accepted Answer

Directed toward the center of the circle

Question 2

Which force provides the necessary centripetal acceleration for a car turning a corner on a level road?

Accepted Answer

Friction

Question 3

A coin is rotating on a turntable without sliding. At the instant shown, which arrow gives the direction of the frictional force on the coin?

Accepted Answer

Radially inward toward the center

Question 4

A 1500 kg car takes a turn around a curve of radius 20 m on a level road. If the coefficient of static friction is 1.0, what is the maximum speed the car can have without sliding?

Accepted Answer

$$v = \sqrt{\mu_s g r} = \sqrt{1.0 	imes 9.8 	imes 20} \approx 14\,	ext{m/s}$$

Question 5

A car moves at a constant speed and goes into a dip in the road, which is part of a circle. At the bottom of the dip, which is bigger: the normal force of the road on the car or the car's weight?

Accepted Answer

The normal force of the road on the car

Question 6

A skateboarder attempts a loop-the-loop in a full pipe with a diameter of 4.3 m. What is the minimum speed required at the very top of the loop to avoid falling?

Accepted Answer

$$v = \sqrt{g r} = \sqrt{9.8 	imes 2.15} \approx 4.6\,	ext{m/s}$$

Question 7

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

Accepted Answer

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

Question 8

If the gravitational force between two asteroids is 1,000,000 N, what will the force be if the distance between them is doubled?

Accepted Answer

250,000 N

Question 9

Planet X has a free-fall acceleration $$g = 8\,	ext{m/s}^2 at $$its surface. Planet Y has twice the mass and twice the radius of Planet X. What is the acceleration due to gravity on Planet Y?

Accepted Answer

$$g = 4\,	ext{m/s}^2$$

Question 10

Two people, each of mass 65 kg, are seated 0.60 m apart. What is the magnitude of the gravitational force between them? ($$G = 6.67 	imes 10$$^{-11}$$\,	ext{N}\cdot	ext{m}^2/	ext{kg}^2)$$

Accepted Answer

$$F = 7.6 	imes 10$$^{-8}$$\,	ext{N}$$

Question 11

A geostationary satellite orbits the Earth so that it appears stationary above the equator. What is the radius of its orbit? (Earth mass $$M_E = 5.98 	imes 10$$^{24}$$\,	ext{kg}$$, $$G = 6.67 	imes 10$$^{-11}$$\,	ext{N}\cdot	ext{m}^2/	ext{kg}^2$$, period $$T = 24$$ hours)

Accepted Answer

$$r = 4.22 	imes 10^7$\,	ext{m}$$

Question 12

Which of the following statements about centrifugal force is correct?

Accepted Answer

It is a fictitious force that arises in non-inertial reference frames.

Question 13

A circular blade of a table saw is 0.30 m in diameter and spins at 120 revolutions per second. What is the speed of a tooth at the edge of the blade?

Accepted Answer

$$v = 2 \pi r f = 2 \pi 	imes 0.15 	imes 120 \approx 113\,	ext{m/s}$$

Question 14

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

Accepted Answer

The one in the smaller orbit

Question 15

Kepler's Third Law relates the period $$T$$ and radius $$r of a $$planet's orbit. Which equation correctly expresses this law for circular orbits?

Accepted Answer

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

Question 16

A car is moving at a constant speed over the top of a hill shaped as a circular arc. At the very top, which force acts downward on the car?

Accepted Answer

Gravity

Question 17

The acceleration of an object in uniform circular motion is given by which formula?

Accepted Answer

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

Question 18

A racetrack curve of radius 70 m is banked at a 15° angle. What is the speed at which a car can take this curve without assistance from friction?

Accepted Answer

$$v = \sqrt{r g 	an 	heta} = \sqrt{70 	imes 9.8 	imes 	an 15^\circ} \approx 14\,	ext{m/s}$$

Chapter 6: Circular Motion, Orbits, and Gravity – Physics for the Life Sciences

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