Q: A 2 kg ball moving at 3 m/s collides elastically with a stationary 1 kg ball. What is the total momentum of the system after the collision?

$$p_{\text{total}} = m_1$ v_{1i} + m_2$ v_{2i} = 2 \times 3 + 1 \times 0 = 6\ \text{kg} \cdot \text{m/s}$$

Q: A 5 kg object is lifted vertically from the ground to a height of 10 m. How much work is done against gravity?

$$W = Fd = mgh = 5 \times 9.8 \times 10 = 490\ \text{J}$$

Q: A 10 kg box falls from a height of 8 m to 2 m. What is the change in its potential energy?

$$\Delta PE = m g (h_f - h_i) = 10 \times 9.8 \times (2 - 8) = -588\ \text{J}$$

Question 1

A 1,200 kg car traveling at 25 m/s crashes into a wall and comes to a stop in 0.2 seconds. What average force did the wall exert on the car?

Accepted Answer

$$F = \frac{\Delta p}{\Delta t} = \frac{m(v_f - v_i)}{\Delta t} = \frac{1200 	imes (0 - 25)}{0.2} = -150,000\ 	ext{N}$$

Question 2

Which of the following best describes a perfectly inelastic collision?

Accepted Answer

Momentum is conserved, but kinetic energy is not; objects stick together after the collision.

Question 3

A 2 kg ball moving at 3 m/s collides elastically with a stationary 1 kg ball. What is the total momentum of the system after the collision?

Accepted Answer

$$p_{	ext{total}} = m_1$ v_{1i} + m_2$ v_{2i} = 2 	imes 3 + 1 	imes 0 = 6\ 	ext{kg} \cdot 	ext{m/s}$$

Question 4

A 5 kg object is lifted vertically from the ground to a height of 10 m. How much work is done against gravity?

Accepted Answer

$$W = Fd = mgh = 5 	imes 9.8 	imes 10 = 490\ 	ext{J}$$

Question 5

If the speed of a moving object triples, by what factor does its kinetic energy increase?

Accepted Answer

It increases by a factor of 9, since $$KE = \frac{1}{2}mv^2$.

Question 6

A 10 kg box falls from a height of 8 m to 2 m. What is the change in its potential energy?

Accepted Answer

$$\Delta PE = m g (h_f - h_i) = 10 	imes 9.8 	imes (2 - 8) = -588\ 	ext{J}$$

Question 7

According to Newton’s Law of Universal Gravitation, what happens to the gravitational force between two objects if the distance between them is tripled?

Accepted Answer

The force becomes one-ninth as large, since $$F = G \frac{m_1$ m_2$}{r^2$}.$$

Question 8

If the radius of a planet shrinks to half its original value but its mass stays the same, how does the surface gravity change?

Accepted Answer

It increases by a factor of 4, since $$g = G \frac{M}{r^2$}.$$

Question 9

Why are astronauts in the International Space Station considered 'weightless'?

Accepted Answer

They are in continuous free fall around Earth, so they experience apparent weightlessness.

Question 10

A 70 kg astronaut and a 140 kg satellite are floating in space. If the astronaut pushes the satellite away at 2 m/s, what is the astronaut’s recoil velocity?

Accepted Answer

$$m_1$$ $$v_1$$ = -$$m_2$$ $$v_2$$ \Rightarrow 70 $$v_1 = -140$$ 	imes 2 \Rightarrow $$v_1 = -4$$\ 	ext{m/s}$$

Question 11

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

Accepted Answer

$$v_f = \frac{m_1$ v_1$ + m_2$ v_2$}{m_1$ + m_2$} = \frac{3 	imes 4 + 2 	imes 0}{3 + 2} = \frac{12}{5} = 2.4\ 	ext{m/s}$$

Question 12

A 60 W light bulb is left on for 5 hours. How much energy does it use?

Accepted Answer

$$E = P t = 60 	imes 5 	imes 3600 = 1,080,000\ 	ext{J}$$

Question 13

A spaceship travels at $$0.8c$$ relative to Earth. If 10 years pass on Earth, how much time passes on the spaceship according to special relativity?

Accepted Answer

$$t' = t \sqrt{1 - v^2$/c^2$$} = 10 	imes 0.6 = 6\ 	ext{years}$

Question 14

According to general relativity, why does time run slower near a black hole?

Accepted Answer

Stronger gravity curves spacetime more, causing time to pass more slowly.

Question 15

Which equation expresses the equivalence of mass and energy, as demonstrated in nuclear reactions?

Accepted Answer

$$E = mc^2$

Question 16

A train car of mass 10,000 kg moving at 2 m/s collides and couples with a stationary car of mass 15,000 kg. What is their speed after coupling?

Accepted Answer

$$v_f = \frac{10,000 	imes 2 + 15,000 	imes 0}{10,000 + 15,000} = \frac{20,000}{25,000} = 0.8\ 	ext{m/s}$$

Question 17

A 1,000 kg satellite orbits Earth at a distance $$r$$ from the center. If its orbital radius is doubled, what happens to the gravitational force it experiences?

Accepted Answer

The force becomes one-fourth as great, since $$F = G \frac{m_1$ m_2$}{r^2$}.$$

Question 18

A rod of length 5 m moves at $$0.6c$$ relative to an observer. What is its observed length?

Accepted Answer

$$L' = L \sqrt{1 - v^2$/c^2$$} = 5 	imes \sqrt{1 - 0.36} = 5 	imes 0.8 = 4\ 	ext{m}$

Question 19

Which of the following best explains why airbags reduce injuries in car crashes?

Accepted Answer

They increase the time over which the force acts, reducing the average force on the person ($$J = F \Delta t).$$

Question 20

A 2 kg object is dropped from a height of 20 m. Ignoring air resistance, what is its speed just before hitting the ground?

Accepted Answer

$$mgh = \frac{1}{2}mv^2$ \Rightarrow v = \sqrt{2gh} = \sqrt{2 	imes 9.8 	imes 20} \approx 19.8\ 	ext{m/s}$$

Accelerated Physics Final Exam Study Guide: Momentum, Energy, Gravity, and Relativity

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