Q: A 10 kg box rests on a horizontal surface. If the coefficient of static friction between the box and the surface is $$\mu_s = 0.5$$, what is the maximum horizontal force that can be applied before the box starts to move?

$$F_{max} = \mu_s N = 0.5 \times 10 \times 9.8 = 49\ \mathrm{N}$$

Q: A car is parked on a hill inclined at $$30^\circ to $$the horizontal. If the coefficient of static friction is $$\mu_s = 0.6$$, will the car stay at rest? (Assume $$g = 9.8\ \mathrm{m/s^2$}$$ and the car's mass is $$1000\ \mathrm{kg}.)$$

Yes, because $$\mu_s N = 0.6 \times 1000 \times 9.8 \times \cos 30^\circ = 5091\ \mathrm{N}$$, which is greater than the downhill force $$1000 \times 9.8 \times \sin 30^\circ = 4900\ \mathrm{N}.$$

Q: A 5 kg block is pulled horizontally with a force of $$30\ \mathrm{N}. $$The coefficient of kinetic friction is $$\mu_k = 0.2. $$What is the acceleration of the block? ($$g = 9.8\ \mathrm{m/s^2$})$$

$$a = \frac{F - \mu_k mg}{m} = \frac{30 - 0.2 \times 5 \times 9.8}{5} = 3.08\ \mathrm{m/s^2$}$$

Q: A 2 kg object is suspended by a rope and remains at rest. What is the tension in the rope? ($$g = 9.8\ \mathrm{m/s^2$})$$

$$T = mg = 2 \times 9.8 = 19.6\ \mathrm{N}$$

Question 1

Which of the following statements best describes the condition for an object to be in equilibrium?

Accepted Answer

The net force acting on the object is zero: $$\sum \vec{F} = 0.$$

Question 2

A 10 kg box rests on a horizontal surface. If the coefficient of static friction between the box and the surface is $$\mu_s = 0.5$$, what is the maximum horizontal force that can be applied before the box starts to move?

Accepted Answer

$$F_{max} = \mu_s N = 0.5 	imes 10 	imes 9.8 = 49\ \mathrm{N}$$

Question 3

Which of the following is NOT a fundamental force of nature?

Accepted Answer

Frictional force

Question 4

A car is parked on a hill inclined at $$30^\circ to $$the horizontal. If the coefficient of static friction is $$\mu_s = 0.6$$, will the car stay at rest? (Assume $$g = 9.8\ \mathrm{m/s^2$}$$ and the car's mass is $$1000\ \mathrm{kg}.)$$

Accepted Answer

Yes, because $$\mu_s N = 0.6 	imes 1000 	imes 9.8 	imes \cos 30^\circ = 5091\ \mathrm{N}$$, which is greater than the downhill force $$1000 	imes 9.8 	imes \sin 30^\circ = 4900\ \mathrm{N}.$$

Question 5

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 objects are sliding and is usually less than the maximum static friction.

Question 6

A 5 kg block is pulled horizontally with a force of $$30\ \mathrm{N}. $$The coefficient of kinetic friction is $$\mu_k = 0.2. $$What is the acceleration of the block? ($$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$a = \frac{F - \mu_k mg}{m} = \frac{30 - 0.2 	imes 5 	imes 9.8}{5} = 3.08\ \mathrm{m/s^2$}$$

Question 7

Which of the following is the correct SI unit for force?

Accepted Answer

$$\mathrm{N} ($$Newton)$$ = \mathrm{kg} \cdot \mathrm{m/s^2$}$$

Question 8

A person pushes a box across a floor at constant velocity. Which statement is true about the forces acting on the box?

Accepted Answer

The applied force is equal in magnitude and opposite in direction to the kinetic friction force.

Question 9

Which of the following is a correct step in drawing a free-body diagram?

Accepted Answer

Represent the object as a point and draw all forces acting on it with arrows showing magnitude and direction.

Question 10

A 2 kg object is suspended by a rope and remains at rest. What is the tension in the rope? ($$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$T = mg = 2 	imes 9.8 = 19.6\ \mathrm{N}$$

Question 11

Which of the following best explains why nuclear forces are not commonly experienced in everyday life?

Accepted Answer

Nuclear forces act only over extremely short distances inside atomic nuclei.

Question 12

A 15 kg crate is at rest on a rough floor. The coefficient of static friction is $$\mu_s = 0.4. $$What is the minimum force required to start moving the crate?

Accepted Answer

$$F_{min} = \mu_s mg = 0.4 	imes 15 	imes 9.8 = 58.8\ \mathrm{N}$$

Question 13

Which of the following is a correct statement about the direction of frictional force?

Accepted Answer

Friction always acts opposite to the direction of relative motion (or attempted motion) between surfaces.

Question 14

A 20 kg box is being pulled up a $$25^\circ$$ incline at constant speed. The coefficient of kinetic friction is $$\mu_k = 0.3. $$What is the magnitude of the frictional force?

Accepted Answer

$$f_k = \mu_k N = 0.3 	imes 20 	imes 9.8 	imes \cos 25^\circ = 53.3\ \mathrm{N}$$

Question 15

Which of the following is a correct example of a normal force?

Accepted Answer

The upward force exerted by the ground on a person standing still.

Question 16

A 50 kg person stands in an elevator that is accelerating upward at $$2\ \mathrm{m/s^2$}. $$What is the normal force exerted by the floor on the person?

Accepted Answer

$$N = m(g + a) = 50 	imes (9.8 + 2) = 590\ \mathrm{N}$$

Question 17

Which of the following is a correct statement about net force?

Accepted Answer

The net force is the vector sum of all forces acting on an object.

Question 18

A 3 kg object is acted on by two forces: $$F_1 = 10$$\ \mathrm{N}$$ to the right and F_2$ = 4\ \mathrm{N} to $$the left. What is the acceleration of the object?

Accepted Answer

$$a = \frac{F_{net}}{m} = \frac{10 - 4}{3} = 2\ \mathrm{m/s^2$}$$

Forces, Free-Body Diagrams, Equilibrium & Friction: Study Notes

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