Q: A 10 kg box is at rest on a horizontal surface. The coefficient of static friction between the box and the surface is 0.4. What is the minimum horizontal force required to start moving the box?

$$F = \mu_s N = 0.4 \times (10 \times 9.8) = 39.2\ \text{N}$$

Q: A 5 kg object is pulled up a frictionless incline at an angle of $$30^\circ$$ with a force parallel to the incline. What is the magnitude of the force required to move the object at constant velocity?

$$F = mg \sin \theta = 5 \times 9.8 \times \sin 30^\circ = 24.5\ \text{N}$$

Q: Which equation correctly represents the net force acting on a mass $$m$$ sliding down a rough incline with angle $$\theta$$ and coefficient of kinetic friction $$\mu_k$$?

$$F_{\text{net}} = mg \sin \theta - \mu_k mg \cos \theta$$

Q: A 2 kg block is attached to a spring (horizontal surface, $$k = 100\ \text{N/m}) $$and pulled so the spring stretches by 0.1 m. What is the force exerted by the spring?

$$F = -kx = -100 \times 0.1 = -10\ \text{N}$$

Q: A 3 kg object is suspended by two ropes, each making a $$45^\circ$$ angle with the ceiling. What is the tension in each rope?

$$T = \frac{mg}{2 \sin 45^\circ} = \frac{3 \times 9.8}{2 \times 0.707} = 20.8\ \text{N}$$

Q: A car of mass 1000 kg is parked on a hill inclined at $$20^\circ. $$What is the magnitude of the force of static friction keeping the car at rest if the coefficient of static friction is 0.5?

$$F_{\text{friction}} = mg \sin \theta = 1000 \times 9.8 \times \sin 20^\circ = 3352\ \text{N}$$

Q: A 4 kg block is pulled across a horizontal surface with a force of 20 N. If the coefficient of kinetic friction is 0.3, what is the acceleration of the block?

$$a = \frac{F - \mu_k mg}{m} = \frac{20 - 0.3 \times 4 \times 9.8}{4} = 2.35\ \text{m/s}^2$$

Question 1

A 10 kg box is at rest on a horizontal surface. The coefficient of static friction between the box and the surface is 0.4. What is the minimum horizontal force required to start moving the box?

Accepted Answer

$$F = \mu_s N = 0.4 	imes (10 	imes 9.8) = 39.2\ 	ext{N}$$

Question 2

Which of the following best describes the normal force acting on an object resting on an inclined plane?

Accepted Answer

It is equal to the perpendicular component of the object's weight: $$N = mg \cos 	heta$$

Question 3

A 5 kg object is pulled up a frictionless incline at an angle of $$30^\circ$$ with a force parallel to the incline. What is the magnitude of the force required to move the object at constant velocity?

Accepted Answer

$$F = mg \sin 	heta = 5 	imes 9.8 	imes \sin 30^\circ = 24.5\ 	ext{N}$$

Question 4

Which equation correctly represents the net force acting on a mass $$m$$ sliding down a rough incline with angle $$	heta$$ and coefficient of kinetic friction $$\mu_k$$?

Accepted Answer

$$F_{	ext{net}} = mg \sin 	heta - \mu_k mg \cos 	heta$$

Question 5

A 2 kg block is attached to a spring (horizontal surface, $$k = 100\ 	ext{N/m}) $$and pulled so the spring stretches by 0.1 m. What is the force exerted by the spring?

Accepted Answer

$$F = -kx = -100 	imes 0.1 = -10\ 	ext{N}$$

Question 6

Which of the following statements about tension in a massless string connecting two objects is correct?

Accepted Answer

The tension is the same throughout the string if the string is massless and frictionless.

Question 7

A 3 kg object is suspended by two ropes, each making a $$45^\circ$$ angle with the ceiling. What is the tension in each rope?

Accepted Answer

$$T = \frac{mg}{2 \sin 45^\circ} = \frac{3 	imes 9.8}{2 	imes 0.707} = 20.8\ 	ext{N}$$

Question 8

Which of the following best describes the direction of the frictional force acting on a moving object?

Accepted Answer

It acts opposite to the direction of motion.

Question 9

A car of mass 1000 kg is parked on a hill inclined at $$20^\circ. $$What is the magnitude of the force of static friction keeping the car at rest if the coefficient of static friction is 0.5?

Accepted Answer

$$F_{	ext{friction}} = mg \sin 	heta = 1000 	imes 9.8 	imes \sin 20^\circ = 3352\ 	ext{N}$$

Question 10

Which of the following is the correct expression for the maximum static friction force?

Accepted Answer

$$f_{s,	ext{max}} = \mu_s N$$

Question 11

A 4 kg block is pulled across a horizontal surface with a force of 20 N. If the coefficient of kinetic friction is 0.3, what is the acceleration of the block?

Accepted Answer

$$a = \frac{F - \mu_k mg}{m} = \frac{20 - 0.3 	imes 4 	imes 9.8}{4} = 2.35\ 	ext{m/s}^2$$

Question 12

Which of the following is NOT a contact force?

Accepted Answer

Gravitational force

Question 13

A 6 kg object is hanging from a rope. What is the tension in the rope if the object is at rest?

Accepted Answer

$$T = mg = 6 	imes 9.8 = 58.8\ 	ext{N}$$

Question 14

A block is at rest on a rough surface. Which of the following statements is true about the forces acting on the block?

Accepted Answer

The normal force balances the weight, and static friction balances any applied horizontal force up to its maximum value.

Question 15

A 2 kg block is connected to a 3 kg block by a massless string over a frictionless pulley. If the system is released from rest, what is the acceleration of the system? (Assume only gravity acts.)

Accepted Answer

$$a = \frac{(3-2) 	imes 9.8}{3+2} = 1.96\ 	ext{m/s}^2$$

Study Notes: Newton's Laws of Motion and Types of Forces

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