Q: A car of mass $$1500\ \mathrm{kg} is $$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?

$$v_{\mathrm{max}} = \sqrt{\mu_s g r} = \sqrt{1.0 \times 9.8 \ \mathrm{m/s^2$} \times 20\ \mathrm{m}} = 14\ \mathrm{m/s}$$

Question 1

A car of mass $$1500\ \mathrm{kg} is $$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

$$v_{\mathrm{max}} = \sqrt{\mu_s g r} = \sqrt{1.0 	imes 9.8 \ \mathrm{m/s^2$} 	imes 20\ \mathrm{m}} = 14\ \mathrm{m/s}$$

Question 2

Which of the following best describes the direction of the acceleration vector for an object in uniform circular motion?

Accepted Answer

It points toward the center of the circle at all times.

Question 3

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

Accepted Answer

$$v = \sqrt{\dfrac{GM_{\mathrm{Earth}}}{r}}$$

Question 4

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

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

Question 5

Which of the following statements about the gravitational force between two masses $$m_1$$ and $$m_2$$ separated by a distance $$r is $$correct?

Accepted Answer

The force is proportional to $$m_1$$ $$m_2$$ and inversely proportional to $$r^2.$$

Question 6

A coin is rotating on a turntable without sliding. If the frictional force suddenly disappears, in what direction will the coin move?

Accepted Answer

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

Question 7

The period $$T of an $$object in uniform circular motion is given by which of the following equations?

Accepted Answer

$$T = \dfrac{2\pi r}{v}$$

Question 8

A 70 kg astronaut weighs less on the Moon than on Earth. If the Moon's mass is $$1/6$$ that of Earth and its radius is $$1/4$$ that of Earth, what is the astronaut's weight on the Moon compared to Earth?

Accepted Answer

The astronaut's weight is $$\dfrac{2}{3} of $$their weight on Earth.

Question 9

A car is moving around a banked curve of radius $$r at an $$angle $$	heta$$ with no friction. What is the correct expression for the speed at which the car can take the curve without sliding?

Accepted Answer

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

Question 10

Which of the following is true about the apparent weight of a person at the bottom of a vertical circular ride?

Accepted Answer

The apparent weight is greater than the true weight.

Question 11

If the net force acting on an object in circular motion is suddenly removed, what path will the object follow?

Accepted Answer

It will move in a straight line tangent to the circle at the point where the force was removed.

Question 12

Which of the following is NOT a property of centripetal force?

Accepted Answer

It is a fictitious force that acts outward on the object.

Question 13

A planet orbits a star in a nearly circular orbit. If the mass of the star doubles but the radius of the orbit remains the same, what happens to the orbital speed of the planet?

Accepted Answer

It increases by a factor of $$\sqrt{2}.$$

Question 14

Which of the following best describes the relationship between the period $$T$$ and the radius $$r$$ for a satellite in circular orbit around a planet of mass $$M$$?

Accepted Answer

$$T^2$$ \propto $$r^3$$

Question 15

A 2 kg object moves in a circle of radius 4 m at a constant speed of 6 m/s. What is the magnitude of the net force acting on the object?

Accepted Answer

$$F = m \dfrac{v^2$}{r} = 2 	imes \dfrac{36}{4} = 18\ \mathrm{N}$$

Question 16

Which of the following is the correct expression for the gravitational force between two objects of masses $$m_1$$ and $$m_2$$ separated by a distance $$r$$?

Accepted Answer

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

Question 17

A person standing on a scale in an elevator accelerating upward at $$a$$ will observe what apparent weight?

Accepted Answer

$$w_{\mathrm{app}} = m(g + a)$$

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

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