Q: A 10.0-kg box rests on a horizontal floor. The coefficient of static friction is 0.40 and the coefficient of kinetic friction is 0.30. What is the maximum horizontal force that can be applied to the box before it starts to move?

$$F_{\text{max}} = \mu_s F_N = 0.40 \times (10.0\,\text{kg} \times 9.8\,\text{m/s}^2) = 39.2\,\text{N}$$

Q: A 0.150-kg ball is swung in a horizontal circle of radius 0.600 m, making 2.00 revolutions per second. What is the magnitude of its centripetal acceleration?

$$a = \$$omega^2$$ R = (2\pi \times 2.00)^2$ \times 0.600 = 94.7\,\text{m/s}^2$$

Q: A 10.0-kg box is pulled along a horizontal surface by a force of 40.0 N applied at a 30.0° angle above the horizontal. The coefficient of kinetic friction is 0.30. What is the acceleration of the box?

$$a = \frac{F_{\text{pull}} \cos\theta - f_k}{m} = \frac{40.0 \cos 30.0^\circ - 0.30 \times (98.0 - 40.0 \sin 30.0^\circ)}{10.0} = 2.3\,\text{m/s}^2$$

Q: A ship is being pulled through a harbor by two tug boats at constant velocity. Each line has a tension of 200,000 N and makes an angle of 28.0° with the direction of motion. What is the magnitude of the drag force on the ship?

$$F_{\text{drag}} = 2 \times 200,000 \cos 28.0^\circ = 353,000\,\text{N}$$

Q: A car travels around a banked curve of radius $$r at $$speed $$v$$ with no friction required. What is the formula for the banking angle $$\theta$$?

$$\tan \theta = \frac{v^2$}{rg}$$

Question 1

A 10.0-kg box rests on a horizontal floor. The coefficient of static friction is 0.40 and the coefficient of kinetic friction is 0.30. What is the maximum horizontal force that can be applied to the box before it starts to move?

Accepted Answer

$$F_{	ext{max}} = \mu_s F_N = 0.40 	imes (10.0\,	ext{kg} 	imes 9.8\,	ext{m/s}^2) = 39.2\,	ext{N}$$

Question 2

A 0.150-kg ball is swung in a horizontal circle of radius 0.600 m, making 2.00 revolutions per second. What is the magnitude of its centripetal acceleration?

Accepted Answer

$$a = \$$omega^2$$ R = (2\pi 	imes 2.00)^2$ 	imes 0.600 = 94.7\,	ext{m/s}^2$$

Question 3

A car of mass 1000 kg rounds a flat curve of radius 50 m at a speed of 15 m/s. If the coefficient of static friction is 0.60, will the car skid?

Accepted Answer

No, because the required friction force $$F = m v^2$ / r = 4500\,	ext{N} is $$less than $$\mu_s F_N = 5880\,	ext{N}.$$

Question 4

Which of the following statements about friction is correct?

Accepted Answer

The maximum static friction force is generally greater than the kinetic friction force for the same surfaces.

Question 5

A 10.0-kg box is pulled along a horizontal surface by a force of 40.0 N applied at a 30.0° angle above the horizontal. The coefficient of kinetic friction is 0.30. What is the acceleration of the box?

Accepted Answer

$$a = \frac{F_{	ext{pull}} \cos	heta - f_k}{m} = \frac{40.0 \cos 30.0^\circ - 0.30 	imes (98.0 - 40.0 \sin 30.0^\circ)}{10.0} = 2.3\,	ext{m/s}^2$$

Question 6

A skydiver of mass $$m$$ falls through air and eventually reaches terminal velocity. If the drag force is proportional to velocity, what is the expression for the terminal velocity?

Accepted Answer

$$v_T = \frac{mg}{b}$$

Question 7

A ship is being pulled through a harbor by two tug boats at constant velocity. Each line has a tension of 200,000 N and makes an angle of 28.0° with the direction of motion. What is the magnitude of the drag force on the ship?

Accepted Answer

$$F_{	ext{drag}} = 2 	imes 200,000 \cos 28.0^\circ = 353,000\,	ext{N}$$

Question 8

Which of the following best describes the direction of the frictional force acting on a box sliding to the right on a rough surface?

Accepted Answer

The frictional force acts to the left, opposite to the direction of motion.

Question 9

A car travels around a banked curve of radius $$r at $$speed $$v$$ with no friction required. What is the formula for the banking angle $$	heta$$?

Accepted Answer

$$	an 	heta = \frac{v^2$}{rg}$$

Question 10

Which of the following statements about uniform circular motion is correct?

Accepted Answer

The speed is constant, but the velocity is not because its direction changes.

Question 11

A ball of mass $$m is $$swung in a vertical circle of radius $$R. $$What is the minimum speed at the top of the circle so that the ball continues in a circle?

Accepted Answer

$$v_{	ext{min}} = \sqrt{gR}$$

Question 12

If the frictional force is insufficient for a car to round a curve, what will happen to the car's path?

Accepted Answer

The car will move more nearly in a straight line, tending to skid outward.

Question 13

Which of the following is true about the force required for uniform circular motion?

Accepted Answer

It is always directed toward the center of the circle.

Question 14

A 10.0-kg box is held against a rough vertical wall by applying a horizontal force. If the coefficient of static friction is 0.40, what is the minimum horizontal force required to keep the box from sliding down?

Accepted Answer

$$F = \frac{mg}{\mu_s} = \frac{10.0 	imes 9.8}{0.40} = 245\,	ext{N}$$

Question 15

Which of the following best describes the difference between static and kinetic friction?

Accepted Answer

Static friction prevents motion up to a maximum value, while kinetic friction acts when there is relative motion.

Question 16

A cyclist is moving at a constant speed in a circle of radius $$R. If $$the speed is doubled, by what factor does the required centripetal force change?

Accepted Answer

It increases by a factor of 4, since $$F_c = m v^2$ / R.$$

Question 17

Which of the following is a correct expression for the period $$T of an $$object in uniform circular motion with frequency $$f$$?

Accepted Answer

$$T = \frac{1}{f}$$

Question 18

A falling object experiences a drag force proportional to its velocity. Which of the following statements is true before the object reaches terminal velocity?

Accepted Answer

The net force is downward and the object accelerates downward.

Chapter 5: Using Newton's Laws – Friction, Uniform Circular Motion, and Drag Forces

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