Q: A 5 kg box slides down a frictionless incline of height 2 m. What is its speed at the bottom?

$$v = \sqrt{2gh} = \sqrt{2 \times 9.8 \times 2} = 6.26\ \mathrm{m/s}$$

Q: A 3 kg block is pushed across a horizontal surface with a force of 15 N over a distance of 4 m. The force is applied at an angle of $$30^\circ$$ above the horizontal. What is the work done by the force?

$$W = 15 \cos 30^\circ \times 4 = 51.96\ \mathrm{J}$$

Q: A 0.5 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?

$$F = m \frac{v^2$}{r} = 0.5 \times \frac{16}{2} = 4\ \mathrm{N}$$

Q: A 2 kg block is attached to a spring (k = 100 N/m) and is compressed 0.1 m from equilibrium. What is the elastic potential energy stored in the spring?

$$U = \frac{1}{2} k x^2$ = 0.5 \times 100 \times 0.01 = 0.5\ \mathrm{J}$$

Q: A 1000 kg car is moving at 20 m/s. What is its momentum?

$$p = m v = 1000 \times 20 = 20000\ \mathrm{kg\cdot m/s}$$

Q: A 2 kg object is dropped from a height of 5 m. What is the change in gravitational potential energy?

$$\Delta U = m g h = 2 \times 9.8 \times 5 = 98\ \mathrm{J}$$

Q: A 2 kg block is moving at 3 m/s. What is its kinetic energy?

$$K = \frac{1}{2} m v^2$ = 0.5 \times 2 \times 9 = 9\ \mathrm{J}$$

Q: A 5 kg object is moving at 2 m/s. If a net force of 10 N acts in the direction of motion for 3 seconds, what is the final speed?

$$v_f = v_i + \frac{F}{m} t = 2 + \frac{10}{5} \times 3 = 8\ \mathrm{m/s}$$

Q: A 0.5 kg ball is dropped from rest and falls 10 m. What is its speed just before hitting the ground? (Neglect air resistance.)

$$v = \sqrt{2gh} = \sqrt{2 \times 9.8 \times 10} = 14\ \mathrm{m/s}$$

Question 1

A 10 kg box rests on a horizontal surface. If a horizontal force of 20 N is applied but the box does not move, and the coefficient of static friction is 0.3, what is the magnitude of the frictional force acting on the box?

Accepted Answer

$$f_s = 20\ \mathrm{N}$$

Question 2

A car of mass $$m is $$rounding a flat curve of radius $$R. If $$the coefficient of static friction between the tires and the road is $$\mu$$, what is the maximum speed $$v_{max} at $$which the car can take the turn without skidding?

Accepted Answer

$$v_{max} = \sqrt{\mu g R}$$

Question 3

A 2 kg object falls through air and eventually reaches terminal speed. If the drag force is given by $$F_{drag} = bv$$, what is the terminal speed $$v_t$$?

Accepted Answer

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

Question 4

A block is attached to a spring with spring constant $$k$$ and is pulled a distance $$x$$ from equilibrium. What is the work done by the spring as the block is released and returns to equilibrium?

Accepted Answer

$$W = \frac{1}{2} k x^2$

Question 5

A 5 kg box slides down a frictionless incline of height 2 m. What is its speed at the bottom?

Accepted Answer

$$v = \sqrt{2gh} = \sqrt{2 	imes 9.8 	imes 2} = 6.26\ \mathrm{m/s}$$

Question 6

A 0.2 kg ball is thrown straight up with an initial speed of 10 m/s. What is its kinetic energy at the highest point?

Accepted Answer

$$K = 0$$

Question 7

A 3 kg block is pushed across a horizontal surface with a force of 15 N over a distance of 4 m. The force is applied at an angle of $$30^\circ$$ above the horizontal. What is the work done by the force?

Accepted Answer

$$W = 15 \cos 30^\circ 	imes 4 = 51.96\ \mathrm{J}$$

Question 8

A 0.5 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

$$F = m \frac{v^2$}{r} = 0.5 	imes \frac{16}{2} = 4\ \mathrm{N}$$

Question 9

A 10 kg box is pulled up a rough incline (angle $$30^\circ) $$with a force parallel to the incline. The coefficient of kinetic friction is 0.2. What is the net force required to move the box up at constant speed?

Accepted Answer

$$F = mg \sin 30^\circ + \mu_k mg \cos 30^\circ$$

Question 10

A 2 kg block is attached to a spring (k = 100 N/m) and is compressed 0.1 m from equilibrium. What is the elastic potential energy stored in the spring?

Accepted Answer

$$U = \frac{1}{2} k x^2$ = 0.5 	imes 100 	imes 0.01 = 0.5\ \mathrm{J}$$

Question 11

A 0.5 kg ball moving at 6 m/s collides elastically with a stationary 0.5 kg ball. What is the velocity of the first ball after the collision?

Accepted Answer

$$v_1$$' = 0\ \mathrm{m/s}$$

Question 12

A 1000 kg car is moving at 20 m/s. What is its momentum?

Accepted Answer

$$p = m v = 1000 	imes 20 = 20000\ \mathrm{kg\cdot m/s}$$

Question 13

A 2 kg object is dropped from a height of 5 m. What is the change in gravitational potential energy?

Accepted Answer

$$\Delta U = m g h = 2 	imes 9.8 	imes 5 = 98\ \mathrm{J}$$

Question 14

A 0.1 kg ball is thrown horizontally at 10 m/s and lands at the same height. What is the work done by gravity during the flight?

Accepted Answer

$$W = 0$$

Question 15

A 2 kg block is moving at 3 m/s. What is its kinetic energy?

Accepted Answer

$$K = \frac{1}{2} m v^2$ = 0.5 	imes 2 	imes 9 = 9\ \mathrm{J}$$

Question 16

A 5 kg object is moving at 2 m/s. If a net force of 10 N acts in the direction of motion for 3 seconds, what is the final speed?

Accepted Answer

$$v_f = v_i + \frac{F}{m} t = 2 + \frac{10}{5} 	imes 3 = 8\ \mathrm{m/s}$$

Question 17

A 0.5 kg ball is dropped from rest and falls 10 m. What is its speed just before hitting the ground? (Neglect air resistance.)

Accepted Answer

$$v = \sqrt{2gh} = \sqrt{2 	imes 9.8 	imes 10} = 14\ \mathrm{m/s}$$

Question 18

A 2 kg block is attached to a spring and oscillates on a frictionless surface. If the maximum speed is 3 m/s and the spring constant is 18 N/m, what is the amplitude of oscillation?

Accepted Answer

$$A = \frac{v_{max}}{\sqrt{k/m}} = \frac{3}{\sqrt{18/2}} = 1\ \mathrm{m}$$

Question 19

A 1000 kg car accelerates from rest to 20 m/s in 10 seconds. What is the average power output if the net force is constant?

Accepted Answer

$$P_{avg} = \frac{\Delta K}{\Delta t} = \frac{1}{2} m v^2$ / t = \frac{1}{2} 	imes 1000 	imes 400 / 10 = 20000\ \mathrm{W}$$

Physics Exam 2 Review: Newton's Laws, Friction, Work, Energy, and Momentum

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