Q: A 1500 kg car is turning around a flat curve of radius $$20\ \mathrm{m}$$ with a coefficient of static friction $$\mu_s = 1.0. $$What is the maximum speed at which the car can make the turn without sliding?

$$v_{max} = \sqrt{\mu_s g r}$$, so $$v_{max} = \sqrt{1.0 \times 9.8 \times 20} = 14\ \mathrm{m/s}$$

Q: A 0.0030 kg sample is spun in an ultracentrifuge with a centripetal acceleration of $$2.45 \times 10^6$\ \mathrm{m/s^2$}. $$What is the apparent weight of the sample?

$$w_{app} = m a = 0.0030 \times 2.45 \times 10^6$ = 7.4\ \mathrm{N}$$

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}$$\ \mathrm{N\cdot m^2$/kg^2$$}$)

$$F = 7.8 \times 10$$^{-7}$$\ \mathrm{N}$$

Question 1

A car is rounding a curve of radius $$r at a $$constant speed $$v. $$What is the direction of the car's acceleration at any instant?

Accepted Answer

Perpendicular to the velocity, pointing toward the center of the curve

Question 2

A 1500 kg car is turning around a flat curve of radius $$20\ \mathrm{m}$$ with a coefficient of static friction $$\mu_s = 1.0. $$What is the maximum speed at which the car can make the turn without sliding?

Accepted Answer

$$v_{max} = \sqrt{\mu_s g r}$$, so $$v_{max} = \sqrt{1.0 	imes 9.8 	imes 20} = 14\ \mathrm{m/s}$$

Question 3

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

Accepted Answer

The static friction force between the tires and the road

Question 4

A satellite orbits Earth at a radius $$r$$ from the center of the planet. What is the expression for its orbital speed?

Accepted Answer

$$v_{orbit} = \sqrt{GM/r}$$

Question 5

A roller coaster car of mass $$m$$ 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 6

A 0.0030 kg sample is spun in an ultracentrifuge with a centripetal acceleration of $$2.45 	imes 10^6$\ \mathrm{m/s^2$}. $$What is the apparent weight of the sample?

Accepted Answer

$$w_{app} = m a = 0.0030 	imes 2.45 	imes 10^6$ = 7.4\ \mathrm{N}$$

Question 7

According to Newton’s law of universal gravitation, what happens to the gravitational force between two masses if the distance between them is doubled?

Accepted Answer

It becomes one-fourth as large

Question 8

A coin sits on a turntable rotating at constant speed. What force keeps the coin moving in a circle?

Accepted Answer

Friction

Question 9

A satellite is in a circular orbit around Earth. If the mass of the satellite is doubled but the orbital radius remains the same, what happens to its orbital speed?

Accepted Answer

It remains the same

Question 10

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}$$\ \mathrm{N\cdot m^2$/kg^2$$}$)

Accepted Answer

$$F = 7.8 	imes 10$$^{-7}$$\ \mathrm{N}$$

Question 11

A car is moving at a constant speed around a banked curve with no friction. What force provides the necessary centripetal acceleration?

Accepted Answer

The horizontal component of the normal force

Question 12

A satellite orbits a planet of mass $$M at a $$radius $$r. $$What is the period $$T of $$its orbit?

Accepted Answer

$$T = 2\pi \sqrt{\dfrac{r^3$}{GM}}$$

Question 13

Why do astronauts in the International Space Station feel weightless?

Accepted Answer

Because they are in free fall around the Earth

Question 14

A ball is tied to a string and swung in a horizontal circle. If the string breaks, what path will the ball follow?

Accepted Answer

It will move in a straight line tangent to the circle at the point of release

Question 15

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

Accepted Answer

The planet with the largest value of $$g$$

Question 16

A car travels over the top of a hill with a radius of curvature $$r at $$speed $$v. $$What is the normal force acting on the car at the top of the hill?

Accepted Answer

$$n = mg - \dfrac{mv^2$}{r}$$

Question 17

If the mass of a planet doubles and its radius also doubles, what happens to the acceleration due to gravity at its surface?

Accepted Answer

It becomes half as much

Question 18

A centrifuge spins a sample in a circle of radius $$r at $$frequency $$f. $$What is the formula for the centripetal acceleration?

Accepted Answer

$$a = 4\pi^2$ f^2$ r$$

Question 19

A satellite is in a circular orbit of radius $$r$$ around a planet of mass $$M. $$What is the gravitational force acting on the satellite?

Accepted Answer

$$F = \dfrac{GMm}{r^2$}$$

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

Study Guide - Practice Questions

Study Guide - Flashcards