$$J = m(v_f - v_i) = 0.15 \times (60 - (-40)) = 0.15 \times 100 = 15\ \mathrm{kg\cdot m/s}$$

$$p_{total} = m_1$ v_1$ + m_2$ v_2$ = 2 \times 5 + 3 \times 0 = 10\ \mathrm{kg\cdot m/s}$$

$$PE = mgh = 5 \times 9.8 \times 4 = 196\ \mathrm{J}$$

$$\text{Efficiency} = \frac{\text{useful output}}{\text{input}} = \frac{500}{800} = 0.625 = 62.5\%$$

Question 1

A 0.15 kg baseball is pitched at 40 m/s and is hit straight back at 60 m/s. What is the impulse delivered to the ball by the bat?

Accepted Answer

$$J = m(v_f - v_i) = 0.15 	imes (60 - (-40)) = 0.15 	imes 100 = 15\ \mathrm{kg\cdot m/s}$$

Question 2

Which of the following best describes the law of conservation of momentum in a closed system?

Accepted Answer

The total momentum before an interaction is equal to the total momentum after the interaction.

Question 3

A 2 kg object moving at 5 m/s collides elastically with a stationary 3 kg object. What is the total momentum of the system after the collision?

Accepted Answer

$$p_{total} = m_1$ v_1$ + m_2$ v_2$ = 2 	imes 5 + 3 	imes 0 = 10\ \mathrm{kg\cdot m/s}$$

Question 4

Which of the following is the correct expression for kinetic energy?

Accepted Answer

$$KE = \frac{1}{2}mv^2$

Question 5

A 5 kg box is lifted vertically 4 m. What is the increase in its gravitational potential energy? (Take $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$PE = mgh = 5 	imes 9.8 	imes 4 = 196\ \mathrm{J}$$

Question 6

Which of the following best describes the work-energy theorem?

Accepted Answer

The net work done on an object is equal to its change in kinetic energy.

Question 7

A machine does 500 J of useful work with an energy input of 800 J. What is its efficiency?

Accepted Answer

$$	ext{Efficiency} = \frac{	ext{useful output}}{	ext{input}} = \frac{500}{800} = 0.625 = 62.5\%$$

Question 8

Which of the following statements about projectile motion is correct?

Accepted Answer

The horizontal and vertical motions are independent of each other.

Question 9

According to the first postulate of special relativity, which of the following is true?

Accepted Answer

The laws of physics are the same in all uniformly moving frames of reference.

Question 10

A spaceship travels at $$0.8c$$ relative to Earth. What is the Lorentz factor $$\gamma$$ for this speed?

Accepted Answer

$$\gamma = \frac{1}{\sqrt{1 - (0.8)^2$}} = \frac{1}{\sqrt{1 - 0.64}} = \frac{1}{\sqrt{0.36}} = \frac{1}{0.6} = 1.67$$

Question 11

Which equation correctly relates mass and energy according to Einstein's theory?

Accepted Answer

$$E = mc^2$

Question 12

A 1,000 kg car moving at 20 m/s collides inelastically with a 1,000 kg car at rest. What is their final velocity after sticking together?

Accepted Answer

$$v_f = \frac{m_1$ v_1$ + m_2$ v_2$}{m_1$ + m_2$} = \frac{1000 	imes 20 + 1000 	imes 0}{2000} = \frac{20000}{2000} = 10\ \mathrm{m/s}$$

Question 13

Which of the following is a consequence of time dilation in special relativity?

Accepted Answer

A moving clock runs slower compared to a stationary clock.

Question 14

A 10 kg object is dropped from a height of 5 m. Ignoring air resistance, what is its speed just before hitting the ground?

Accepted Answer

$$v = \sqrt{2gh} = \sqrt{2 	imes 9.8 	imes 5} = \sqrt{98} \approx 9.9\ \mathrm{m/s}$$

Question 15

Which of the following best describes the correspondence principle?

Accepted Answer

New theories must agree with old theories where the old theories give correct results.

Question 16

A 60 W light bulb is left on for 2 hours. How much energy does it use in joules?

Accepted Answer

$$E = P 	imes t = 60 	imes (2 	imes 3600) = 60 	imes 7200 = 432000\ \mathrm{J}$$

Question 17

Which of the following is true for an elastic collision?

Accepted Answer

Both momentum and kinetic energy are conserved.

Question 18

A 0.5 kg ball is thrown straight up with an initial speed of 10 m/s. What is its maximum height?

Accepted Answer

$$h = \frac{v^2$}{2g} = \frac{10^2$}{2 	imes 9.8} = \frac{100}{19.6} \approx 5.1\ \mathrm{m}$$

Question 19

Which of the following is NOT a simple machine?

Accepted Answer

A battery

Physics Study Guide: Momentum, Energy, Projectile Motion, and Special Relativity

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