Q: A 2 kg block is pushed across a frictionless surface with a constant force of 10 N for a distance of 5 m. What is the work done on the block?

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

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

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

Q: A ball of mass $$0.5\ \mathrm{kg} is $$dropped from a height of $$10\ \mathrm{m}. $$Ignoring air resistance, what is its velocity just before hitting the ground?

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

Q: A $$1\ \mathrm{kg}$$ object is attached to a spring and oscillates with a maximum speed of $$2\ \mathrm{m/s}. $$What is its maximum kinetic energy?

$$K_{max} = \frac{1}{2} m v^2$ = \frac{1}{2} \times 1 \times 2^2$ = 2\ \mathrm{J}$$

Q: Which statement about mechanical energy in a system with only conservative forces is correct?

Mechanical energy is conserved: $$E_{mech} = K + U = \text{constant}$$

Q: A $$0.5\ \mathrm{kg}$$ ball is thrown vertically upward with an initial speed of $$8\ \mathrm{m/s}. $$What is its maximum height?

$$h_{max} = \frac{v^2$}{2g} = \frac{8^2$}{2 \times 9.8} \approx 3.27\ \mathrm{m}$$

Q: A $$3\ \mathrm{kg}$$ object moving at $$4\ \mathrm{m/s}$$ collides inelastically with a $$2\ \mathrm{kg}$$ object moving at $$-2\ \mathrm{m/s}. $$What is their final velocity?

$$v_f = \frac{3 \times 4 + 2 \times (-2)}{3 + 2} = \frac{12 - 4}{5} = 1.6\ \mathrm{m/s}$$

Question 1

A 2 kg block is pushed across a frictionless surface with a constant force of 10 N for a distance of 5 m. What is the work done on the block?

Accepted Answer

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

Question 2

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

Accepted Answer

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

Question 3

A ball of mass $$0.5\ \mathrm{kg} is $$dropped from a height of $$10\ \mathrm{m}. $$Ignoring air resistance, what is its velocity just before hitting the ground?

Accepted Answer

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

Question 4

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: $$W_{net} = \Delta K$$

Question 5

A car of mass $$1000\ \mathrm{kg}$$ traveling at $$20\ \mathrm{m/s}$$ collides with a stationary car of mass $$1500\ \mathrm{kg}$$ and they stick together. What is their final velocity after the collision?

Accepted Answer

$$v_f = \frac{m_1$ v_1$ + m_2$ v_2$}{m_1$ + m_2$} = \frac{1000 	imes 20 + 1500 	imes 0}{1000 + 1500} = 8\ \mathrm{m/s}$$

Question 6

Which of the following is a conservative force?

Accepted Answer

Gravitational force

Question 7

A $$0.2\ \mathrm{kg}$$ ball moving at $$5\ \mathrm{m/s}$$ collides elastically with a $$0.3\ \mathrm{kg}$$ ball at rest. What is the velocity of the $$0.2\ \mathrm{kg}$$ ball after the collision?

Accepted Answer

$$v_1$$' = \frac{$$m_1$$ - $$m_2$$}{$$m_1$$ + $$m_2$$} $$v_1$$ = \frac{0.2 - 0.3}{0.2 + 0.3} 	imes 5 = -1\ \mathrm{m/s}$$

Question 8

A $$1\ \mathrm{kg}$$ object is attached to a spring and oscillates with a maximum speed of $$2\ \mathrm{m/s}. $$What is its maximum kinetic energy?

Accepted Answer

$$K_{max} = \frac{1}{2} m v^2$ = \frac{1}{2} 	imes 1 	imes 2^2$ = 2\ \mathrm{J}$$

Question 9

Which statement about mechanical energy in a system with only conservative forces is correct?

Accepted Answer

Mechanical energy is conserved: $$E_{mech} = K + U = 	ext{constant}$$

Question 10

A $$0.5\ \mathrm{kg}$$ ball is thrown vertically upward with an initial speed of $$8\ \mathrm{m/s}. $$What is its maximum height?

Accepted Answer

$$h_{max} = \frac{v^2$}{2g} = \frac{8^2$}{2 	imes 9.8} \approx 3.27\ \mathrm{m}$$

Question 11

A $$3\ \mathrm{kg}$$ object moving at $$4\ \mathrm{m/s}$$ collides inelastically with a $$2\ \mathrm{kg}$$ object moving at $$-2\ \mathrm{m/s}. $$What is their final velocity?

Accepted Answer

$$v_f = \frac{3 	imes 4 + 2 	imes (-2)}{3 + 2} = \frac{12 - 4}{5} = 1.6\ \mathrm{m/s}$$

Question 12

A $$0.4\ \mathrm{kg}$$ ball moving at $$3\ \mathrm{m/s}$$ collides elastically with a $$0.6\ \mathrm{kg}$$ ball at rest. What is the velocity of the $$0.6\ \mathrm{kg}$$ ball after the collision?

Accepted Answer

$$v_2$$' = \frac{2 $$m_1$$}{$$m_1$$ + $$m_2$$} $$v_1$$ = \frac{2 	imes 0.4}{0.4 + 0.6} 	imes 3 = 2.4\ \mathrm{m/s}$$

Question 13

A $$5\ \mathrm{kg}$$ object is lifted vertically $$2\ \mathrm{m} at $$constant speed. What is the work done by gravity?

Accepted Answer

$$W_{gravity} = -mgh = -5 	imes 9.8 	imes 2 = -98\ \mathrm{J}$$

Question 14

Which of the following scenarios best illustrates the conservation of mechanical energy?

Accepted Answer

A pendulum swinging without air resistance

Question 15

A $$0.3\ \mathrm{kg}$$ ball is dropped from a height of $$5\ \mathrm{m}. $$What is its kinetic energy just before it hits the ground?

Accepted Answer

$$K = mgh = 0.3 	imes 9.8 	imes 5 = 14.7\ \mathrm{J}$$

Question 16

A $$2\ \mathrm{kg}$$ object moving at $$6\ \mathrm{m/s}$$ collides with a $$3\ \mathrm{kg}$$ object at rest. If the collision is perfectly elastic, what is the velocity of the $$2\ \mathrm{kg}$$ object after the collision?

Accepted Answer

$$v_1$$' = \frac{$$m_1$$ - $$m_2$$}{$$m_1$$ + $$m_2$$} $$v_1$$ = \frac{2 - 3}{2 + 3} 	imes 6 = -1.2\ \mathrm{m/s}$$

Question 17

Which of the following is true about impulse?

Accepted Answer

Impulse is equal to the change in momentum: $$J = \Delta p$$

Question 18

A $$0.5\ \mathrm{kg}$$ ball moving at $$4\ \mathrm{m/s} is $$stopped in $$0.2\ \mathrm{s} by a $$constant force. What is the magnitude of the force?

Accepted Answer

$$F = \frac{\Delta p}{\Delta t} = \frac{0.5 	imes 4}{0.2} = 10\ \mathrm{N}$$

Study Guide: Kinetic Energy, Work, Potential Energy, and Linear Momentum

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