Q: A 1200 kg car travels around a flat, circular track of radius 60 m in 30 seconds without slipping. What is the magnitude of the static friction force acting on the car?

$$F = m a_R = m \frac{v^2$}{r} = 1200 \times \frac{(2\pi \times 60/30)^2$}{60} = 1200 \times \frac{(4\pi)^2$}{60} \approx 3160\ \mathrm{N}$$

Q: A race car starts from rest and reaches a speed of $$35\ \mathrm{m/s} in$$ $$11\ \mathrm{s} on a $$circular track of radius $$500\ \mathrm{m}. $$What is the magnitude of the tangential acceleration?

$$a_{\text{tan}} = \frac{35}{11} \approx 3.18\ \mathrm{m/s^2$}$$

Q: A 1.5 × $$10^6 kg $$asteroid is positioned halfway between the Earth ($$M_E = 5.98 \times 10$$^{24}$$ kg) and the Moon (M_M = 7.35$$ \times $$10^{22} kg$$), with the average distance between Earth and Moon being $$3.84 \times 10^8$ m. What is the net gravitational force on the asteroid?

$$F = G m \left( \frac{M_E}{(1.92 \times 10^8$)^2$$} - \frac{M_M}{(1.92 \times $$10^8)^2$} \right)$$

Question 1

A 1200 kg car travels around a flat, circular track of radius 60 m in 30 seconds without slipping. What is the magnitude of the static friction force acting on the car?

Accepted Answer

$$F = m a_R = m \frac{v^2$}{r} = 1200 	imes \frac{(2\pi 	imes 60/30)^2$}{60} = 1200 	imes \frac{(4\pi)^2$}{60} \approx 3160\ \mathrm{N}$$

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 perpendicular to the velocity and points toward the center of the circle.

Question 3

A satellite orbits the Earth at a height $$h$$ above the surface. If the radius of the Earth is $$R_E$$, what is the speed $$v of $$the satellite in terms of $$G$$, $$M_E$$, $$R_E$$, and $$h$$?

Accepted Answer

$$v = \sqrt{\frac{G M_E}{R_E + h}}$$

Question 4

A car is rounding a banked curve of radius $$r at $$the ideal speed so that no friction is required. If the banking angle is $$	heta$$, what is the ideal speed $$v$$?

Accepted Answer

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

Question 5

Which of the following statements about 'weightlessness' experienced by astronauts in orbit is correct?

Accepted Answer

The astronauts are in free fall, so they experience apparent weightlessness.

Question 6

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

The force becomes one-fourth as large.

Question 7

A race car starts from rest and reaches a speed of $$35\ \mathrm{m/s} in$$ $$11\ \mathrm{s} on a $$circular track of radius $$500\ \mathrm{m}. $$What is the magnitude of the tangential acceleration?

Accepted Answer

$$a_{	ext{tan}} = \frac{35}{11} \approx 3.18\ \mathrm{m/s^2$}$$

Question 8

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

Accepted Answer

Friction

Question 9

A 1.5 × $$10^6 kg $$asteroid is positioned halfway between the Earth ($$M_E = 5.98 	imes 10$$^{24}$$ kg) and the Moon (M_M = 7.35$$ 	imes $$10^{22} kg$$), with the average distance between Earth and Moon being $$3.84 	imes 10^8$ m. What is the net gravitational force on the asteroid?

Accepted Answer

$$F = G m \left( \frac{M_E}{(1.92 	imes 10^8$)^2$$} - \frac{M_M}{(1.92 	imes $$10^8)^2$} ight)$$

Question 10

Kepler’s Second Law states that:

Accepted Answer

A planet sweeps out equal areas in equal times as it orbits the Sun.

Question 11

A ball on a string is 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 12

The acceleration due to gravity $$g at $$the surface of the Earth can be expressed as:

Accepted Answer

$$g = \frac{G M_E}{R_E^2$}$$

Question 13

A centrifuge separates substances by spinning them rapidly. What is the primary force responsible for this separation?

Accepted Answer

Centripetal force

Question 14

If the static friction coefficient between a car’s tires and a flat road is $$\mu_s$$, what is the maximum speed $$v_{max}$$ the car can have without skidding on a curve of radius $$r$$?

Accepted Answer

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

Question 15

Which of the following best explains why the normal force is zero for an astronaut in orbit?

Accepted Answer

Both the astronaut and the spacecraft are in free fall around the Earth.

Question 16

Which of the following is a correct statement of Newton’s Law of Universal Gravitation?

Accepted Answer

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

Question 17

A planet orbits a star at a mean distance $$r$$ with period $$T. $$According to Kepler’s Third Law, which equation is correct?

Accepted Answer

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

Question 18

A car is moving around a curve and begins to skid. Which of the following statements is true?

Accepted Answer

The frictional force has become kinetic and is now less than the required centripetal force.

Chapter 5: Circular Motion and Gravitation – Study Notes

Study Guide - Practice Questions

Study Guide - Flashcards