Q: A car of mass $$1500\ \mathrm{kg}$$ turns a corner of radius $$20\ \mathrm{m} on a $$level road with a coefficient of static friction $$\mu_s = 1.0. $$What is the maximum speed $$v_{\text{max}}$$ the car can have without sliding?

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

Question 1

A particle moves in uniform circular motion with constant speed $$v$$ and radius $$r. $$Which of the following statements is TRUE about its velocity and acceleration vectors?

Accepted Answer

The velocity vector is tangent to the circle, and the acceleration vector is directed toward the center of the circle.

Question 2

A table saw blade has a diameter of $$0.25\ \mathrm{m}$$ and spins at $$3600\ \mathrm{rpm}. $$What is the period $$T$$ for one revolution of the blade?

Accepted Answer

$$T = \dfrac{1}{3600}\ \mathrm{s}$$

Question 3

A car of mass $$1500\ \mathrm{kg}$$ turns a corner of radius $$20\ \mathrm{m} on a $$level road with a coefficient of static friction $$\mu_s = 1.0. $$What is the maximum speed $$v_{	ext{max}}$$ the car can have without sliding?

Accepted Answer

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

Question 4

A coin is rotating on a turntable without sliding. At a given instant, if the frictional force suddenly disappears, what path will the coin follow?

Accepted Answer

It will move in a straight line tangent to the circle at that instant.

Question 5

A car is at the bottom of a dip in the road, moving at constant speed. How does the normal force $$n$$ from the road compare to the car’s weight $$w at $$this point?

Accepted Answer

$$n \u003e w$$

Question 6

A car is turning a corner at constant speed on a flat road. What force provides the necessary centripetal acceleration?

Accepted Answer

The static friction force between the tires and the road

Question 7

A curve on a racetrack of radius $$70\ \mathrm{m} is $$banked at $$15^\circ. If $$there is no friction, what is the correct formula for the speed $$v at $$which a car can take the curve?

Accepted Answer

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

Question 8

Astronauts on the International Space Station feel weightless because:

Accepted Answer

They are in free fall.

Question 9

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 10

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

Accepted Answer

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

Question 11

A satellite orbits Earth in a circular orbit of radius $$r. $$What is the correct expression for its orbital speed $$v$$?

Accepted Answer

$$v = \sqrt{\dfrac{G M}{r}}$$

Question 12

Two satellites have circular orbits with the same radius around Earth. One satellite has twice the mass of the other. Which statement is correct?

Accepted Answer

Both satellites have the same speed.

Question 13

A car of mass $$m$$ goes over a hill of radius $$r at $$speed $$v. $$What is the normal force $$n$$ exerted by the road on the car at the top of the hill?

Accepted Answer

$$n = m g - \dfrac{m v^2$}{r}$$

Question 14

A projectile is launched horizontally from a high altitude with a speed such that the curvature of its trajectory matches that of the Earth. What is the nature of its motion?

Accepted Answer

It will enter a circular orbit around the Earth.

Question 15

The period $$T of a $$satellite in a circular orbit of radius $$r$$ around a planet of mass $$M is $$given by:

Accepted Answer

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

Question 16

If the mass of the Earth were doubled but its radius remained the same, what would happen to the acceleration due to gravity $$g at $$the surface?

Accepted Answer

$$g$$ would double.

Question 17

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

Accepted Answer

On the planet with the largest mass and smallest radius.

Question 18

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

Accepted Answer

The satellite’s period

Question 19

A handful of professional skaters have taken a skateboard through an inverted loop in a full pipe of radius $$2\ \mathrm{m}. $$What is the minimum speed $$v_c$$ the skater must have at the very top of the loop to avoid falling?

Accepted Answer

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

Circular Motion, Orbits, and Gravity: Study Notes for Physics with Calculus

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