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

Guida di studio - Domande di pratica

Study guide - Flashcard