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

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

Q: A car of mass 1200 kg is moving at a constant speed of 20 m/s around a flat, circular track of radius 50 m. What is the magnitude of the frictional force required to keep the car moving in a circle?

$$F = m a_c = m \frac{v^2$}{r} = 1200 \times \frac{20^2$}{50} = 9600\ \text{N}$$

Q: A 5 kg block is pulled across a horizontal surface with a constant velocity by a horizontal force of 20 N. What is the coefficient of kinetic friction between the block and the surface?

$$\mu_k = \frac{F}{mg} = \frac{20}{5 \times 9.8} \approx 0.41$$

Q: A skydiver of mass 80 kg reaches terminal velocity during free fall. If the drag force is proportional to the square of the velocity, what is the magnitude of the drag force at terminal velocity?

$$F_{\text{drag}} = mg = 80 \times 9.8 = 784\ \text{N}$$

Q: A block of mass 2 kg is at rest on a horizontal table. The coefficient of static friction between the block and the table is 0.4. What is the minimum horizontal force required to start moving the block?

$$F_{\text{min}} = \mu_s mg = 0.4 \times 2 \times 9.8 = 7.84\ \text{N}$$

Q: A 3 kg object moves in a circle of radius 2 m at a constant speed of 4 m/s. What is the magnitude of the net force acting on the object?

$$F = m \frac{v^2$}{r} = 3 \times \frac{16}{2} = 24\ \text{N}$$

Q: A 15 kg ladder leans against a frictionless wall, making a 60° angle with the ground. The coefficient of static friction between the ladder and the ground is 0.3. What is the minimum frictional force required at the base to prevent slipping?

$$f_{\text{min}} = \mu_s mg = 0.3 \times 15 \times 9.8 = 44.1\ \text{N}$$

Q: A 2 kg puck slides on a horizontal ice rink with an initial speed of 5 m/s. If the coefficient of kinetic friction between the puck and the ice is 0.1, how far will the puck travel before coming to rest?

$$d = \frac{v^2$}{2 \mu_k g} = \frac{25}{2 \times 0.1 \times 9.8} \approx 12.76\ \text{m}$$

Question 1

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

Accepted Answer

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

Question 2

A car of mass 1200 kg is moving at a constant speed of 20 m/s around a flat, circular track of radius 50 m. What is the magnitude of the frictional force required to keep the car moving in a circle?

Accepted Answer

$$F = m a_c = m \frac{v^2$}{r} = 1200 	imes \frac{20^2$}{50} = 9600\ 	ext{N}$$

Question 3

Which of the following statements about free-body diagrams is correct?

Accepted Answer

The acceleration vector $$\vec{a}$$ should not be included in a free-body diagram because it is not a force.

Question 4

A 5 kg block is pulled across a horizontal surface with a constant velocity by a horizontal force of 20 N. What is the coefficient of kinetic friction between the block and the surface?

Accepted Answer

$$\mu_k = \frac{F}{mg} = \frac{20}{5 	imes 9.8} \approx 0.41$$

Question 5

A skydiver of mass 80 kg reaches terminal velocity during free fall. If the drag force is proportional to the square of the velocity, what is the magnitude of the drag force at terminal velocity?

Accepted Answer

$$F_{	ext{drag}} = mg = 80 	imes 9.8 = 784\ 	ext{N}$$

Question 6

A block of mass 2 kg is at rest on a horizontal table. The coefficient of static friction between the block and the table is 0.4. What is the minimum horizontal force required to start moving the block?

Accepted Answer

$$F_{	ext{min}} = \mu_s mg = 0.4 	imes 2 	imes 9.8 = 7.84\ 	ext{N}$$

Question 7

A 3 kg object moves in a circle of radius 2 m at a constant speed of 4 m/s. What is the magnitude of the net force acting on the object?

Accepted Answer

$$F = m \frac{v^2$}{r} = 3 	imes \frac{16}{2} = 24\ 	ext{N}$$

Question 8

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

Accepted Answer

Static friction acts when there is no relative motion between surfaces, while kinetic friction acts when surfaces slide past each other.

Question 9

A 15 kg ladder leans against a frictionless wall, making a 60° angle with the ground. The coefficient of static friction between the ladder and the ground is 0.3. What is the minimum frictional force required at the base to prevent slipping?

Accepted Answer

$$f_{	ext{min}} = \mu_s mg = 0.3 	imes 15 	imes 9.8 = 44.1\ 	ext{N}$$

Question 10

A 2 kg puck slides on a horizontal ice rink with an initial speed of 5 m/s. If the coefficient of kinetic friction between the puck and the ice is 0.1, how far will the puck travel before coming to rest?

Accepted Answer

$$d = \frac{v^2$}{2 \mu_k g} = \frac{25}{2 	imes 0.1 	imes 9.8} \approx 12.76\ 	ext{m}$$

Question 11

A 0.5 kg ball is attached to a string and whirled in a horizontal circle of radius 1.5 m at a speed of 3 m/s. If the string breaks, what will be the motion of the ball immediately after the break?

Accepted Answer

The ball will move in a straight line tangent to the circle at the point of release.

Question 12

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

Accepted Answer

Frictional force

Question 13

A 4 kg block is pulled up a 30° incline with a force parallel to the incline. The coefficient of kinetic friction is 0.2. What is the magnitude of the frictional force acting on the block?

Accepted Answer

$$f_k = \mu_k N = 0.2 	imes 4 	imes 9.8 	imes \cos(30^\circ) \approx 6.79\ 	ext{N}$$

Question 14

A 50 kg crate is at rest on a horizontal floor. The coefficient of static friction is 0.6. What is the minimum force required to start moving the crate?

Accepted Answer

$$F_{	ext{min}} = \mu_s mg = 0.6 	imes 50 	imes 9.8 = 294\ 	ext{N}$$

Question 15

A cyclist is moving at a constant speed on a level road. Which statement best describes the net force acting on the cyclist?

Accepted Answer

The net force is zero because the cyclist is in equilibrium (constant velocity).

Question 16

A 10 kg object is suspended by two ropes that make equal angles with the ceiling. If the object is at rest, what is the tension in each rope?

Accepted Answer

$$T = \frac{mg}{2 \cos 	heta}$$, where $$	heta is $$the angle each rope makes with the ceiling.

Question 17

A 2 kg block is pushed up a frictionless incline at an angle of 25° with an acceleration of 2 m/s². What is the net force acting parallel to the incline?

Accepted Answer

$$F_{	ext{net}} = m a = 2 	imes 2 = 4\ 	ext{N}$$

Question 18

A 0.2 kg rubber eraser is pressed against a dry concrete wall with a normal force of 5 N. If the coefficient of static friction is 1.0, what is the maximum frictional force that can act on the eraser?

Accepted Answer

$$f_{s,	ext{max}} = \mu_s N = 1.0 	imes 5 = 5\ 	ext{N}$$

Applying Newton’s Laws: Forces, Friction, and Circular Motion

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