Q: A 2 kg block is pushed by a constant force of 10 N over a distance of 5 m along a horizontal surface. If the force is applied parallel to the displacement and there is no friction, what is the work done by the force?

$$W = F \times d = 10 \times 5 = 50\ \text{J}$$

Q: A car of mass 1000 kg accelerates from rest to a speed of 20 m/s. What is its kinetic energy at this speed?

$$KE = \frac{1}{2} m v^2$ = \frac{1}{2} \times 1000 \times 20^2$ = 200,000\ \text{J}$$

Q: A 0.5 kg ball is dropped from a height of 10 m. Ignoring air resistance, what is its speed just before hitting the ground? (Use $$g = 9.8\ \text{m/s}^2)$$

$$v = \sqrt{2 g h} = \sqrt{2 \times 9.8 \times 10} \approx 14\ \text{m/s}$$

Q: A spring with force constant $$k = 200\ \text{N/m} is $$compressed by 0.1 m. What is the elastic potential energy stored in the spring?

$$U = \frac{1}{2} k x^2$ = \frac{1}{2} \times 200 \times (0.1)^2$ = 1\ \text{J}$$

Q: A 3 kg object moves with a velocity of $$4\ \text{m/s}$$ east. What is its momentum?

$$p = m v = 3 \times 4 = 12\ \text{kg}\cdot\text{m/s}$$\ \text{east}$

Q: A 2 kg object is acted upon by a net force of 6 N for 3 seconds. What is the impulse delivered to the object?

$$J = F \Delta t = 6 \times 3 = 18\ \text{N}\cdot\text{s}$$

Q: A 2 kg object is dropped from a height of 8 m. If it lands with a speed of $$12\ \text{m/s}$$, how much energy was lost to air resistance?

$$\Delta E = m g h - \frac{1}{2} m v^2$ = 2 \times 9.8 \times 8 - \frac{1}{2} \times 2 \times 12^2$ = 156.8 - 144 = 12.8\ \text{J}$$

Q: A 5 kg object is moving at $$2\ \text{m/s}$$ and is stopped by a constant force over a distance of 4 m. What is the magnitude of the force required?

$$F = \frac{\Delta KE}{d} = \frac{\frac{1}{2} \times 5 \times 2^2$}{4} = \frac{10}{4} = 2.5\ \text{N}$$

Q: A 0.2 kg ball is thrown vertically upward with a speed of $$10\ \text{m/s}. $$What is its maximum height above the launch point? (Ignore air resistance, $$g = 9.8\ \text{m/s}^2)$$

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

Question 1

A 2 kg block is pushed by a constant force of 10 N over a distance of 5 m along a horizontal surface. If the force is applied parallel to the displacement and there is no friction, what is the work done by the force?

Accepted Answer

$$W = F 	imes d = 10 	imes 5 = 50\ 	ext{J}$$

Question 2

A car of mass 1000 kg accelerates from rest to a speed of 20 m/s. What is its kinetic energy at this speed?

Accepted Answer

$$KE = \frac{1}{2} m v^2$ = \frac{1}{2} 	imes 1000 	imes 20^2$ = 200,000\ 	ext{J}$$

Question 3

A 0.5 kg ball is dropped from a height of 10 m. Ignoring air resistance, what is its speed just before hitting the ground? (Use $$g = 9.8\ 	ext{m/s}^2)$$

Accepted Answer

$$v = \sqrt{2 g h} = \sqrt{2 	imes 9.8 	imes 10} \approx 14\ 	ext{m/s}$$

Question 4

A spring with force constant $$k = 200\ 	ext{N/m} is $$compressed by 0.1 m. What is the elastic potential energy stored in the spring?

Accepted Answer

$$U = \frac{1}{2} k x^2$ = \frac{1}{2} 	imes 200 	imes (0.1)^2$ = 1\ 	ext{J}$$

Question 5

A 3 kg object moves with a velocity of $$4\ 	ext{m/s}$$ east. What is its momentum?

Accepted Answer

$$p = m v = 3 	imes 4 = 12\ 	ext{kg}\cdot	ext{m/s}$$\ 	ext{east}$

Question 6

A 2 kg object is acted upon by a net force of 6 N for 3 seconds. What is the impulse delivered to the object?

Accepted Answer

$$J = F \Delta t = 6 	imes 3 = 18\ 	ext{N}\cdot	ext{s}$$

Question 7

A 1 kg ball moving at $$5\ 	ext{m/s}$$ collides elastically with a stationary 1 kg ball. What is the velocity of the first ball after the collision?

Accepted Answer

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

Question 8

A 2 kg object is dropped from a height of 8 m. If it lands with a speed of $$12\ 	ext{m/s}$$, how much energy was lost to air resistance?

Accepted Answer

$$\Delta E = m g h - \frac{1}{2} m v^2$ = 2 	imes 9.8 	imes 8 - \frac{1}{2} 	imes 2 	imes 12^2$ = 156.8 - 144 = 12.8\ 	ext{J}$$

Question 9

A 5 kg object is moving at $$2\ 	ext{m/s}$$ and is stopped by a constant force over a distance of 4 m. What is the magnitude of the force required?

Accepted Answer

$$F = \frac{\Delta KE}{d} = \frac{\frac{1}{2} 	imes 5 	imes 2^2$}{4} = \frac{10}{4} = 2.5\ 	ext{N}$$

Question 10

A 0.2 kg ball is thrown vertically upward with a speed of $$10\ 	ext{m/s}. $$What is its maximum height above the launch point? (Ignore air resistance, $$g = 9.8\ 	ext{m/s}^2)$$

Accepted Answer

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

Question 11

A 1 kg object moves from $$x = 0 to$$ $$x = 4 m $$under a force $$F(x) = 3x. $$What is the work done by the force?

Accepted Answer

$$W = \int_{0}^{4} 3x\ dx = 3 \int_{0}^{4} x\ dx = 3 \left[ \frac{1}{2} x^2$ ight]_{0}^{4} = 3 	imes 8 = 24\ 	ext{J}$$

Question 12

A 2 kg object is moving at $$3\ 	ext{m/s}$$ and collides inelastically with a stationary 2 kg object. What is their final velocity after the collision?

Accepted Answer

$$v_f = \frac{m_1$ v_1$ + m_2$ v_2$}{m_1$ + m_2$} = \frac{2 	imes 3 + 2 	imes 0}{2 + 2} = \frac{6}{4} = 1.5\ 	ext{m/s}$$

Question 13

A 0.5 kg object is attached to a spring with $$k = 100\ 	ext{N/m}$$ and is pulled to $$x = 0.2 m. $$What is the force exerted by the spring?

Accepted Answer

$$F = -k x = -100 	imes 0.2 = -20\ 	ext{N}$$

Question 14

A 3 kg object is moving at $$6\ 	ext{m/s}$$ and is brought to rest in 2 seconds. What is the average power required to stop the object?

Accepted Answer

$$P = \frac{\Delta KE}{\Delta t} = \frac{\frac{1}{2} 	imes 3 	imes 6^2$}{2} = \frac{54}{2} = 27\ 	ext{W}$$

Question 15

A 2 kg object is moving at $$4\ 	ext{m/s}$$ north and a 3 kg object is moving at $$2\ 	ext{m/s}$$ east. What is the magnitude of the total momentum of the system?

Accepted Answer

$$p_{	ext{total}} = \sqrt{(2 	imes 4)^2$ + (3 	imes 2)^2$} = \sqrt{8^2$ + 6^2$} = \sqrt{64 + 36} = \sqrt{100} = 10\ 	ext{kg}\cdot	ext{m/s}$$

Question 16

A 1 kg object is at $$y = 5 m $$above the ground. What is its gravitational potential energy relative to the ground? (Use $$g = 9.8\ 	ext{m/s}^2)$$

Accepted Answer

$$U = m g y = 1 	imes 9.8 	imes 5 = 49\ 	ext{J}$$

Question 17

A 2 kg object is acted upon by a net external force of 10 N for 4 seconds. What is its change in momentum?

Accepted Answer

$$\Delta p = F_{	ext{net}} \Delta t = 10 	imes 4 = 40\ 	ext{kg}\cdot	ext{m/s}$$

Question 18

Two particles, one of mass 2 kg at position $$x_1 = 1$ m and another of mass 3 kg at x_2$ = 5 m$$, form a system. What is the center of mass position?

Accepted Answer

$$x_{	ext{cm}} = \frac{m_1$ x_1$ + m_2$ x_2$}{m_1$ + m_2$} = \frac{2 	imes 1 + 3 	imes 5}{2 + 3} = \frac{2 + 15}{5} = \frac{17}{5} = 3.4\ 	ext{m}$$

Work, Energy, and Momentum: Study Guide for PHYS 141 Exam 2 (Chapters 6–8)

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