Q: A car of mass $m$ moves at speed $v$ around a banked curve of radius $r$ with banking angle $\theta$. If no friction is required, what must be true?

$\tan \theta = \dfrac{v^2}{r g}$

Q: Two people, one of mass $50\ \mathrm{kg}$ and the other $70\ \mathrm{kg}$, sit $0.5\ \mathrm{m}$ apart. What is the magnitude of the gravitational force between them? ($G = 6.67 \times 10^{-11}\ \mathrm{N\cdot m^2/kg^2}$)

$F = 6.67 \times 10^{-11} \dfrac{50 \times 70}{0.5^2} \approx 9.3 \times 10^{-8}\ \mathrm{N}$

Question 1

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

Accepted Answer

Velocity is tangent to the circle; acceleration is perpendicular to velocity and points toward the center.

Question 2

A car travels around a flat curve of radius $r = 50\ \mathrm{m}$ with a coefficient of static friction $\mu_s = 0.60$. What is the maximum speed $v_{max}$ the car can have before skidding?

Accepted Answer

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

Question 3

What is the magnitude of the centripetal acceleration $a_c$ for an object moving at constant speed $v$ in a circle of radius $r$?

Accepted Answer

$a_c = \dfrac{v^2}{r}$

Question 4

A ball of mass $m$ is swung in a vertical circle of radius $r$. What is the minimum speed $v_{min}$ at the top of the circle to keep the string taut?

Accepted Answer

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

Question 5

If the period $T$ of an object in circular motion is 5 seconds, what is its frequency $f$?

Accepted Answer

$f = \dfrac{1}{T} = 0.2\ \mathrm{Hz}$

Question 6

A car of mass $m$ moves at speed $v$ around a banked curve of radius $r$ with banking angle $	heta$. If no friction is required, what must be true?

Accepted Answer

$	an 	heta = \dfrac{v^2}{r g}$

Question 7

Which force provides the centripetal force for a car turning on a flat road?

Accepted Answer

Static friction between the tires and the road

Question 8

According to Newton's Law of Universal Gravitation, what is the gravitational force $F$ between two masses $m_1$ and $m_2$ separated by distance $r$?

Accepted Answer

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

Question 9

The acceleration due to gravity at the surface of the Earth is approximately $9.8\ \mathrm{m/s^2}$. Which equation best explains this value?

Accepted Answer

$g = G \dfrac{M_{Earth}}{R_{Earth}^2}$

Question 10

Two people, one of mass $50\ \mathrm{kg}$ and the other $70\ \mathrm{kg}$, sit $0.5\ \mathrm{m}$ apart. 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

$F = 6.67 	imes 10^{-11} \dfrac{50 	imes 70}{0.5^2} \approx 9.3 	imes 10^{-8}\ \mathrm{N}$

Question 11

A race car accelerates uniformly from rest to $35\ \mathrm{m/s}$ on a circular track of radius $500\ \mathrm{m}$. What is the magnitude of the total acceleration when the car reaches $35\ \mathrm{m/s}$, if the tangential acceleration is $2\ \mathrm{m/s^2}$?

Accepted Answer

$a_{total} = \sqrt{a_t^2 + a_c^2}$, where $a_c = \dfrac{v^2}{r}$

Question 12

The Moon orbits the Earth at a radius of $3.84 	imes 10^8\ \mathrm{m}$ and period $T = 27.3$ days. What is the acceleration of the Moon toward Earth?

Accepted Answer

$a = \dfrac{4 \pi^2 r}{T^2}$

Question 13

If the coefficient of static friction on a road drops from $0.60$ to $0.25$ due to ice, what happens to the maximum safe speed for a car rounding a curve of radius $r$?

Accepted Answer

It decreases, since $v_{max} = \sqrt{\mu_s g r}$ and $\mu_s$ is smaller.

Question 14

Which of the following statements about centripetal force is correct?

Accepted Answer

It is not a new type of force, but the name given to the net force causing circular motion.

Question 15

A ball of mass $0.150\ \mathrm{kg}$ is swung in a vertical circle of radius $1.10\ \mathrm{m}$. What is the tension in the cord at the bottom of the arc if the speed is $6.57\ \mathrm{m/s}$?

Accepted Answer

$T = m g + m \dfrac{v^2}{r}$

Question 16

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

Accepted Answer

Frictional force

Question 17

If the gravitational force between two objects is $F$, what happens to $F$ if the distance between them is doubled?

Accepted Answer

It becomes $F/4$

Question 18

A satellite orbits Earth at a height where the acceleration due to gravity is $g'$. If the radius of the orbit is $2 R_{Earth}$, what is $g'$ in terms of $g$ at Earth's surface?

Accepted Answer

$g' = \dfrac{g}{4}$

Circular Motion and Gravitation: Study Notes

Study Guide - Practice Questions

Study Guide - Flashcards