Q: A 10.0-kg box rests on a horizontal floor. The coefficient of static friction between the box and the floor is 0.40, and the coefficient of kinetic friction is 0.30. What is the maximum force of static friction that can act on the box?

$$F_{fr, max} = \mu_s F_N = 0.40 \times 98.0\ \mathrm{N} = 39.2\ \mathrm{N}$$

Q: A 0.150-kg ball is swung in a vertical circle of radius 1.10 m. What is the minimum speed at the top of the circle for the ball to maintain its circular path?

$$v_{min} = \sqrt{g r} = \sqrt{9.8 \times 1.10} = 3.3\ \mathrm{m/s}$$

Q: A skier descends a 30° slope at constant speed. What is the coefficient of kinetic friction between the skis and the snow?

$$\mu_k = \tan 30^\circ = 0.58$$

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

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

Q: A 0.150-kg ball at the end of a string is revolving uniformly in a horizontal circle of radius 0.600 m at 2.00 revolutions per second. What is the centripetal force acting on the ball?

$$F_R = m \frac{v^2$}{r} = 0.150 \times \frac{(7.54)^2$}{0.600} = 14.2\ \mathrm{N}$$

Question 1

A 10.0-kg box rests on a horizontal floor. The coefficient of static friction between the box and the floor is 0.40, and the coefficient of kinetic friction is 0.30. What is the maximum force of static friction that can act on the box?

Accepted Answer

$$F_{fr, max} = \mu_s F_N = 0.40 	imes 98.0\ \mathrm{N} = 39.2\ \mathrm{N}$$

Question 2

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

Accepted Answer

No, because the maximum static friction force is greater than the required centripetal force.

Question 3

Which of the following correctly describes the direction of the acceleration for an object in uniform circular motion?

Accepted Answer

It is always directed toward the center of the circle.

Question 4

A 0.150-kg ball is swung in a vertical circle of radius 1.10 m. What is the minimum speed at the top of the circle for the ball to maintain its circular path?

Accepted Answer

$$v_{min} = \sqrt{g r} = \sqrt{9.8 	imes 1.10} = 3.3\ \mathrm{m/s}$$

Question 5

A skier descends a 30° slope at constant speed. What is the coefficient of kinetic friction between the skis and the snow?

Accepted Answer

$$\mu_k = 	an 30^\circ = 0.58$$

Question 6

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

$$a = \frac{F_{Px} - F_{fr}}{m} = \frac{34.64\ \mathrm{N} - 23.4\ \mathrm{N}}{10.0\ \mathrm{kg}} = 1.12\ \mathrm{m/s^2$}$$

Question 7

Which of the following statements about friction is correct?

Accepted Answer

The coefficient of static friction is usually greater than the coefficient of kinetic friction for the same surfaces.

Question 8

A 4.00-kg object falls with a drag force proportional to its speed. If its acceleration is 3.00 m/s² downward when falling at 20.0 m/s, what is its terminal velocity?

Accepted Answer

$$v_T = \frac{mg}{b} = \frac{39.2\ \mathrm{N}}{1.36\ \mathrm{Ns/m}} = 28.8\ \mathrm{m/s}$$

Question 9

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

Accepted Answer

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

Question 10

A 0.150-kg ball at the end of a string is revolving uniformly in a horizontal circle of radius 0.600 m at 2.00 revolutions per second. What is the centripetal force acting on the ball?

Accepted Answer

$$F_R = m \frac{v^2$}{r} = 0.150 	imes \frac{(7.54)^2$}{0.600} = 14.2\ \mathrm{N}$$

Question 11

A race car starts from rest and accelerates at a uniform rate to a speed of 35 m/s in 11 s, moving on a circular track of radius 250 m. What is the tangential acceleration?

Accepted Answer

$$a_{tan} = \frac{\Delta v}{\Delta t} = \frac{35}{11} = 3.18\ \mathrm{m/s^2$}$$

Question 12

Which of the following best describes terminal velocity for an object falling through a fluid?

Accepted Answer

It is the constant speed at which the drag force equals the gravitational force.

Question 13

A box is held against a rough vertical wall by applying a horizontal force. Which force prevents the box from sliding down?

Accepted Answer

The static friction force between the box and the wall.

Question 14

A car of mass $$m$$ travels at speed $$v$$ around a flat curve of radius $$r. $$What is the minimum coefficient of static friction required to prevent skidding?

Accepted Answer

$$\mu_s = \frac{v^2$}{r g}$$

Question 15

Which of the following is true about the force required to keep an object moving in a circle at constant speed?

Accepted Answer

It must always be directed toward the center of the circle.

Question 16

A conical pendulum consists of a ball of mass $$m$$ suspended by a cord of length $$\ell$$, revolving in a horizontal circle of radius $$r = \ell \sin 	heta. $$What is the correct expression for the speed of the ball?

Accepted Answer

$$v = \sqrt{g \ell \sin 	heta 	an 	heta}$$

Question 17

If a car is moving too fast on a banked curve designed for a lower speed, what will happen if there is no friction?

Accepted Answer

The car will slide up the banked curve.

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

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