Q: A 10-kg box rests on a horizontal floor. The coefficient of static friction between the box and the floor is 0.4, and the coefficient of kinetic friction is 0.3. What is the maximum horizontal force that can be applied to the box before it starts to slide?

$$F_{max} = \mu_s F_N = 0.4 \times (10 \times 9.8) = 39.2\ \mathrm{N}$$

Q: A 20-kg box is pulled along a horizontal surface with a force of 40 N applied at a 30° angle above the horizontal. The coefficient of kinetic friction is 0.3. What is the acceleration of the box?

$$a = \frac{F_{\text{net}}}{m} = \frac{40 \cos 30^\circ - \mu_k (mg - 40 \sin 30^\circ)}{20}$$

Q: A ball of mass 0.5 kg is swung in a horizontal circle of radius 0.6 m, making 2 revolutions per second. What is the centripetal acceleration?

$$a = \$$omega^2$$ R = (2 \pi \times 2)^2$ \times 0.6 = 189.6\ \mathrm{m/s^2$}$$

Q: A ship is being pulled through a harbor by two tugboats, each with a tension of 200,000 N at an angle of 28° to the direction of motion. What is the magnitude of the drag force on the ship?

$$F_{drag} = 2 \times 200,000 \cos 28^\circ$$

Question 1

A 10-kg box rests on a horizontal floor. The coefficient of static friction between the box and the floor is 0.4, and the coefficient of kinetic friction is 0.3. What is the maximum horizontal force that can be applied to the box before it starts to slide?

Accepted Answer

$$F_{max} = \mu_s F_N = 0.4 	imes (10 	imes 9.8) = 39.2\ \mathrm{N}$$

Question 2

Which statement best describes the direction of the frictional force acting on a sled being pulled across snow?

Accepted Answer

The frictional force acts parallel to the surface and opposite to the direction of motion.

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 between the tires and the road is 0.5, will the car skid?

Accepted Answer

No, because the required centripetal force $$F_c = \frac{mv^2$}{r} = \frac{1000 	imes 15^2$}{50} = 4500\ \mathrm{N} is $$less than the maximum static friction $$F_{s,max} = \mu_s F_N = 0.5 	imes 1000 	imes 9.8 = 4900\ \mathrm{N}.$$

Question 4

Which of the following is true about the coefficients of friction for most material pairs?

Accepted Answer

The coefficient of static friction $$\mu_s is $$generally greater than the coefficient of kinetic friction $$\mu_k.$$

Question 5

A 20-kg box is pulled along a horizontal surface with a force of 40 N applied at a 30° angle above the horizontal. The coefficient of kinetic friction is 0.3. What is the acceleration of the box?

Accepted Answer

$$a = \frac{F_{	ext{net}}}{m} = \frac{40 \cos 30^\circ - \mu_k (mg - 40 \sin 30^\circ)}{20}$$

Question 6

Which of the following best explains why it is generally easier to keep an object sliding than to get it started?

Accepted Answer

Because the coefficient of kinetic friction $$\mu_k is $$less than the coefficient of static friction $$\mu_s.$$

Question 7

A falling object experiences a drag force proportional to its velocity. What is the terminal velocity $$v_t of $$the object if its mass is $$m$$ and the drag coefficient is $$b$$?

Accepted Answer

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

Question 8

In uniform circular motion, what is the direction of the acceleration vector?

Accepted Answer

It points toward the center of the circle (centripetal acceleration).

Question 9

A ball of mass 0.5 kg is swung in a horizontal circle of radius 0.6 m, making 2 revolutions per second. What is the centripetal acceleration?

Accepted Answer

$$a = \$$omega^2$$ R = (2 \pi 	imes 2)^2$ 	imes 0.6 = 189.6\ \mathrm{m/s^2$}$$

Question 10

A ship is being pulled through a harbor by two tugboats, each with a tension of 200,000 N at an angle of 28° to the direction of motion. What is the magnitude of the drag force on the ship?

Accepted Answer

$$F_{drag} = 2 	imes 200,000 \cos 28^\circ$$

Question 11

Which of the following is NOT a correct statement about friction?

Accepted Answer

Friction always acts in the direction of motion.

Question 12

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

Accepted Answer

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

Question 13

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 opposes motion once sliding has started.

Question 14

If the centripetal force acting on an object in uniform circular motion suddenly vanishes, what happens to the object?

Accepted Answer

It moves in a straight line tangent to the circle at that point.

Question 15

A 0.5-kg ball is swung in a vertical circle of radius 1 m. What is the minimum speed at the top of the circle to keep the string taut?

Accepted Answer

$$v_{min} = \sqrt{gR} = \sqrt{9.8 	imes 1} = 3.13\ \mathrm{m/s}$$

Question 16

Which of the following is a correct statement about drag forces at high speeds?

Accepted Answer

The drag force is approximately proportional to the square of the velocity.

Question 17

A frog is sitting on a slope. Which direction does the static friction force point?

Accepted Answer

Uphill, opposing the tendency to slide down.

Question 18

Which of the following is the correct formula for the magnitude of centripetal acceleration in uniform circular motion?

Accepted Answer

$$a = \frac{v^2$}{R}$$

Question 19

A 1000-kg car rounds a curve of radius 50 m at a speed of 20 m/s. What is the required centripetal force?

Accepted Answer

$$F_c = \frac{mv^2$}{r} = \frac{1000 	imes 20^2$}{50} = 8000\ \mathrm{N}$$

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

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