Q: A 1200 kg car can accelerate from rest to 100 km/h in 8.0 seconds. What is the maximum net force exerted on the car during this acceleration? (Assume 1 km/h = 0.278 m/s)

$$F = m a = 1200 \times \frac{(100 \times 0.278)}{8} = 1200 \times 3.475 = 4170 \text{ N}$$

Q: A 0.5 kg object is lifted by a person from rest to a height of 2 m in 1.5 s. What is the average power delivered by the person?

$$P = \frac{W}{t} = \frac{mgh}{t} = \frac{0.5 \times 9.8 \times 2}{1.5} = \frac{9.8}{1.5} \approx 6.53 \text{ W}$$

Q: A 0.5 kg object is dropped from a height of 10 m. What is its velocity just before hitting the ground? (Ignore air resistance)

$$v = \sqrt{2gh} = \sqrt{2 \times 9.8 \times 10} = \sqrt{196} = 14 \text{ m/s}$$

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

$$KE = \frac{1}{2} m v^2$ = \frac{1}{2} \times 2 \times 3^2$ = 1 \times 9 = 9 \text{ J}$$

Q: A 0.5 kg object is thrown vertically upward with an initial velocity of 10 m/s. What is the maximum height it reaches? (Ignore air resistance)

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

Q: A 1 kg object is moving in a circle of radius 2 m at a speed of 4 m/s. What is the centripetal force acting on it?

$$F_c = \frac{m v^2$}{r} = \frac{1 \times 16}{2} = 8 \text{ N}$$

Q: A 0.5 kg block slides down a frictionless incline of height 3 m. What is its speed at the bottom?

$$v = \sqrt{2gh} = \sqrt{2 \times 9.8 \times 3} = \sqrt{58.8} \approx 7.67 \text{ m/s}$$

Question 1

A 1200 kg car can accelerate from rest to 100 km/h in 8.0 seconds. What is the maximum net force exerted on the car during this acceleration? (Assume 1 km/h = 0.278 m/s)

Accepted Answer

$$F = m a = 1200 	imes \frac{(100 	imes 0.278)}{8} = 1200 	imes 3.475 = 4170 	ext{ N}$$

Question 2

A rocket is launched vertically upward with a constant acceleration. If the rocket reaches a height of 500 m in 10 s, what is the acceleration of the rocket? (Assume initial velocity is zero)

Accepted Answer

$$s = ut + \frac{1}{2} a t^2$ \Rightarrow 500 = 0 + \frac{1}{2} a (10)^2$ \Rightarrow a = \frac{500}{50} = 10 	ext{ m/s}^2$$

Question 3

A 0.5 kg object is lifted by a person from rest to a height of 2 m in 1.5 s. What is the average power delivered by the person?

Accepted Answer

$$P = \frac{W}{t} = \frac{mgh}{t} = \frac{0.5 	imes 9.8 	imes 2}{1.5} = \frac{9.8}{1.5} \approx 6.53 	ext{ W}$$

Question 4

The acceleration due to gravity on Planet X is non-identical to that on Planet B. If the radius of Planet B is twice that of Planet X, what fraction of Planet B's mass is the mass of Planet X? (Assume $$g = \frac{GM}{R^2$})$$

Accepted Answer

$$\frac{M_X}{M_B} = \frac{g_X R_X^2$}{g_B R_B^2$}$$

Question 5

A 0.5 kg block is moving at 5.0 m/s on a frictionless surface. It collides with a stationary 0.5 kg block and sticks to it. What is the final velocity of the combined blocks?

Accepted Answer

$$v_f = \frac{m_1$ v_1$ + m_2$ v_2$}{m_1$ + m_2$} = \frac{0.5 	imes 5 + 0.5 	imes 0}{1.0} = \frac{2.5}{1.0} = 2.5 	ext{ m/s}$$

Question 6

A 0.5 kg object is dropped from a height of 10 m. What is its velocity just before hitting the ground? (Ignore air resistance)

Accepted Answer

$$v = \sqrt{2gh} = \sqrt{2 	imes 9.8 	imes 10} = \sqrt{196} = 14 	ext{ m/s}$$

Question 7

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

Accepted Answer

$$KE = \frac{1}{2} m v^2$ = \frac{1}{2} 	imes 2 	imes 3^2$ = 1 	imes 9 = 9 	ext{ J}$$

Question 8

A 0.5 kg object is thrown vertically upward with an initial velocity of 10 m/s. What is the maximum height it reaches? (Ignore air resistance)

Accepted Answer

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

Question 9

A 1 kg object is moving in a circle of radius 2 m at a speed of 4 m/s. What is the centripetal force acting on it?

Accepted Answer

$$F_c = \frac{m v^2$}{r} = \frac{1 	imes 16}{2} = 8 	ext{ N}$$

Question 10

A 0.5 kg block slides down a frictionless incline of height 3 m. What is its speed at the bottom?

Accepted Answer

$$v = \sqrt{2gh} = \sqrt{2 	imes 9.8 	imes 3} = \sqrt{58.8} \approx 7.67 	ext{ m/s}$$

Question 11

A 2 kg object is dropped from a height of 5 m. What is the work done by gravity?

Accepted Answer

$$W = mgh = 2 	imes 9.8 	imes 5 = 98 	ext{ J}$$

Question 12

A 0.5 kg object is moving at 2 m/s. What is its momentum?

Accepted Answer

$$p = m v = 0.5 	imes 2 = 1 	ext{ kg m/s}$$

Question 13

A 1 kg object is moving at 3 m/s and collides elastically with a stationary 1 kg object. What is the velocity of the first object after the collision?

Accepted Answer

$$v_1$$' = \frac{$$m_1$$ - $$m_2$$}{$$m_1$$ + $$m_2$$} $$v_1$$ + \frac{2 $$m_2$$}{$$m_1$$ + $$m_2$$} $$v_2$$ = \frac{1 - 1}{2} 	imes 3 + \frac{2 	imes 1}{2} 	imes 0 = 0$$

Question 14

A 0.5 kg object is thrown horizontally from a height of 20 m with a speed of 5 m/s. How long does it take to hit the ground?

Accepted Answer

$$t = \sqrt{\frac{2h}{g}} = \sqrt{\frac{40}{9.8}} \approx 2.02 	ext{ s}$$

Question 15

A 1 kg object is moving at 2 m/s. What is its kinetic energy?

Accepted Answer

$$KE = \frac{1}{2} m v^2$ = \frac{1}{2} 	imes 1 	imes 4 = 2 	ext{ J}$$

Question 16

A 0.5 kg object is moving at 4 m/s. What is its momentum?

Accepted Answer

$$p = m v = 0.5 	imes 4 = 2 	ext{ kg m/s}$$

Question 17

A 2 kg object is moving at 5 m/s. What is its kinetic energy?

Accepted Answer

$$KE = \frac{1}{2} m v^2$ = \frac{1}{2} 	imes 2 	imes 25 = 1 	imes 25 = 25 	ext{ J}$$

Physics 107: Midterm 2 Study Guidance

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