Q: A 1500 kg car is turning a corner of radius 20 m on a level road. If the coefficient of static friction between the tires and the road is $$\mu_s = 0.8$$, what is the maximum speed at which the car can make the turn without sliding?

$$v_{max} = \sqrt{\mu_s g r} = \sqrt{0.8 \times 9.8 \times 20} \approx 12.5\ \mathrm{m/s}$$

Q: A 65 kg student and a 65 kg friend are sitting 0.60 m apart. What is the magnitude of the gravitational force between them?

$$F = \frac{G m_1$ m_2$}{r^2$} = \frac{6.67 \times 10$$^{-11}$$ \times 65 \times 65}{0.6^2$} \approx 7.8 \times 10$$^{-7}$$\ \mathrm{N}$$

Question 1

A 1500 kg car is turning a corner of radius 20 m on a level road. If the coefficient of static friction between the tires and the road is $$\mu_s = 0.8$$, what is the maximum speed at which the car can make the turn without sliding?

Accepted Answer

$$v_{max} = \sqrt{\mu_s g r} = \sqrt{0.8 	imes 9.8 	imes 20} \approx 12.5\ \mathrm{m/s}$$

Question 2

A 65 kg student and a 65 kg friend are sitting 0.60 m apart. What is the magnitude of the gravitational force between them?

Accepted Answer

$$F = \frac{G m_1$ m_2$}{r^2$} = \frac{6.67 	imes 10$$^{-11}$$ 	imes 65 	imes 65}{0.6^2$} \approx 7.8 	imes 10$$^{-7}$$\ \mathrm{N}$$

Question 3

Which force provides the centripetal acceleration for a car turning a corner on a dry road?

Accepted Answer

Static friction between the tires and the road

Question 4

A ball of mass $$m is $$attached to a massless string and swung in a horizontal circle of radius $$r at $$constant speed $$v. $$What is the tension $$T in $$the string?

Accepted Answer

$$T = \frac{m v^2$}{r}$$

Question 5

A satellite orbits just above the surface of the Earth (radius $$R_E) $$with orbital speed $$v_{orb}. $$What is the correct expression for $$v_{orb}$$?

Accepted Answer

$$v_{orb} = \sqrt{g R_E}$$

Question 6

A 100 kg stagehand and a 200 kg stage set are connected by a massless rope over a frictionless pulley. If the stage set is released, what is the acceleration of the stagehand?

Accepted Answer

$$a = \frac{m_{set} - m_{hand}}{m_{set} + m_{hand}} g = \frac{200 - 100}{200 + 100} 	imes 9.8 \approx 3.3\ \mathrm{m/s^2$}$$

Question 7

What is the period $$T of an $$object moving in a circle of radius $$r at $$speed $$v$$?

Accepted Answer

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

Question 8

If the distance between two masses is doubled, what happens to the gravitational force between them according to Newton's law of gravity?

Accepted Answer

It decreases by a factor of 4

Question 9

A roller coaster passenger at the bottom of a vertical loop feels an apparent weight greater than her true weight. What is the correct expression for her apparent weight $$W_{app} at $$the bottom?

Accepted Answer

$$W_{app} = n = w + \frac{m v^2$}{r}$$

Question 10

A mass $$m is $$whirled in a vertical circle of radius $$r. At $$the top of the circle, what is the minimum speed $$v_c$$ required for the mass to maintain contact with the circle?

Accepted Answer

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

Question 11

Which of the following statements about tension in a massless rope passing over a massless, frictionless pulley is correct?

Accepted Answer

The tension is the same on both sides of the pulley

Question 12

A hard drive disk rotates at 7200 rpm. If the disk has a radius of 0.065 m, what is the acceleration of a point on the edge?

Accepted Answer

$$a = v^2$ / r = (2 \pi f r)^2$ / r = 4 \pi^2$ f^2$ r$$;\ f = 7200/60 = 120\ \mathrm{Hz}$$, so a = 4$$ \$$pi^2$$ 	imes $$120^2$$ 	imes 0.065 \approx 14,800\ \mathrm{$$m/s^2$$}$

Question 13

Which of the following is true about the net force in uniform circular motion?

Accepted Answer

It is directed toward the center of the circle and has magnitude $$F = m v^2$ / r$$

Question 14

A mass $$m is $$attached to a rope and swings in a vertical circle. At the bottom of the circle, what is the tension $$T in $$the rope?

Accepted Answer

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

Question 15

Which of the following best describes the sensation of weightlessness experienced by astronauts in orbit?

Accepted Answer

They are in continuous free fall around the Earth, so they feel weightless

Question 16

A box is pulled by a massless rope with force $$F. $$What is the tension $$T in $$the rope?

Accepted Answer

$$T = F$$

Question 17

A car is driving on an icy, frictionless road and tries to turn a corner. What will happen?

Accepted Answer

The car will continue in a straight line due to lack of static friction

Question 18

Which of the following is NOT a property of Newton's law of universal gravitation?

Accepted Answer

The force is inversely proportional to the cube of the distance between objects

Physics for Life Sciences I – Lecture 10: Forces, Ropes & Pulleys, Circular Motion, and Gravitation

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