Q: A 2 kg block slides down a frictionless incline from a height of 5 m. What is its speed at the bottom of the incline? (Assume $$g = 9.8\ \mathrm{m/s^2$}.)$$

$$v = \sqrt{2gh} = \sqrt{2 \times 9.8 \times 5} = 9.9\ \mathrm{m/s}$$

Q: A 0.2 kg ball is dropped from a height of 2 m. What is the impulse delivered to the ball by the floor if it rebounds upward at the same speed it hit the floor? (Take $$g = 9.8\ \mathrm{m/s^2$}.)$$

$$J = 2mv = 2 \times 0.2 \times \sqrt{2 \times 9.8 \times 2} = 2 \times 0.2 \times 6.26 = 2.51\ \mathrm{kg\cdot m/s}$$

Q: A force acts on a 5 kg object for 2 seconds, changing its velocity from 3 m/s to 7 m/s. What is the average force applied?

$$F = m\frac{\Delta v}{\Delta t} = 5 \times \frac{7-3}{2} = 10\ \mathrm{N}$$

Q: A 1 kg object moves with velocity $$\vec{v} = (3\hat{i} + 4\hat{j})\ \mathrm{m/s}. $$What is its kinetic energy?

$$K = \frac{1}{2}mv^2$ = \frac{1}{2} \times 1 \times (3^2$ + 4^2$) = 12.5\ \mathrm{J}$$

Question 1

A 2 kg block slides down a frictionless incline from a height of 5 m. What is its speed at the bottom of the incline? (Assume $$g = 9.8\ \mathrm{m/s^2$}.)$$

Accepted Answer

$$v = \sqrt{2gh} = \sqrt{2 	imes 9.8 	imes 5} = 9.9\ \mathrm{m/s}$$

Question 2

A car of mass $$M$$ collides head-on with a parked truck of mass $$3M. If $$the collision is perfectly elastic and the car was initially moving at $$v_0$$, what is the final velocity of the car?

Accepted Answer

$$v = -\frac{1}{2}v_0$

Question 3

A force $$F(x) = 3x^2$ N acts on a particle along the x-axis. How much work is done by this force as the particle moves from x = 1$ m to x = 3$ m?

Accepted Answer

$$W = \int_{1}^{3} 3x^2$ dx = [x^3$]_{1}^{3} = 27 - 1 = 26\ \mathrm{J}$$

Question 4

A 0.2 kg ball is dropped from a height of 2 m. What is the impulse delivered to the ball by the floor if it rebounds upward at the same speed it hit the floor? (Take $$g = 9.8\ \mathrm{m/s^2$}.)$$

Accepted Answer

$$J = 2mv = 2 	imes 0.2 	imes \sqrt{2 	imes 9.8 	imes 2} = 2 	imes 0.2 	imes 6.26 = 2.51\ \mathrm{kg\cdot m/s}$$

Question 5

Which of the following best describes the relationship between force and work?

Accepted Answer

$$W = \vec{F} \cdot \vec{d}$$

Question 6

A spring with spring constant $$k is $$stretched by a distance $$x. $$What is the potential energy stored in the spring?

Accepted Answer

$$U = \frac{1}{2}kx^2$

Question 7

A bullet of mass $$m is $$fired vertically into a block of mass $$M$$ suspended by a string. The bullet embeds in the block. What principle allows you to find the maximum height the block rises?

Accepted Answer

Conservation of momentum during collision, then conservation of energy after

Question 8

Which of the following is NOT a valid unit for work?

Accepted Answer

$$\mathrm{kg\cdot m/s}$$

Question 9

A force acts on a 5 kg object for 2 seconds, changing its velocity from 3 m/s to 7 m/s. What is the average force applied?

Accepted Answer

$$F = m\frac{\Delta v}{\Delta t} = 5 	imes \frac{7-3}{2} = 10\ \mathrm{N}$$

Question 10

Which of the following statements about impulse is correct?

Accepted Answer

Impulse equals the change in momentum: $$J = \Delta p$$

Question 11

A person pushes a box up a ramp at constant speed. Which of the following is true about the work done by the person?

Accepted Answer

The work done equals the increase in gravitational potential energy

Question 12

Which of the following is a correct statement about the conservation of mechanical energy?

Accepted Answer

Mechanical energy is conserved if only conservative forces do work

Question 13

A 1 kg object moves with velocity $$\vec{v} = (3\hat{i} + 4\hat{j})\ \mathrm{m/s}. $$What is its kinetic energy?

Accepted Answer

$$K = \frac{1}{2}mv^2$ = \frac{1}{2} 	imes 1 	imes (3^2$ + 4^2$) = 12.5\ \mathrm{J}$$

Question 14

Which of the following best describes an inelastic collision?

Accepted Answer

Kinetic energy is not conserved, but momentum is conserved

Question 15

A block slides across a rough surface and comes to rest. Which energy transformation occurs?

Accepted Answer

Kinetic energy is transformed into thermal energy

Question 16

A force $$F$$ acts at an angle $$	heta to $$the direction of displacement $$d. $$What is the work done?

Accepted Answer

$$W = Fd\cos	heta$$

Question 17

Which of the following is a correct expression for power?

Accepted Answer

$$P = \frac{dW}{dt}$$

Question 18

A 3 kg object moving at 4 m/s collides and sticks to a 2 kg object at rest. What is their final velocity?

Accepted Answer

$$v_f = \frac{3 	imes 4 + 2 	imes 0}{3 + 2} = 2.4\ \mathrm{m/s}$$

Question 19

Which of the following is a location of stable equilibrium on a potential energy curve?

Accepted Answer

A minimum of the potential energy curve

Physics I: Study Guide – Energy, Power, Impulse, and Momentum

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