Q: A 2 kg ball is dropped from a height of 50 m. Ignoring air resistance, what is the speed of the ball just before it hits the ground? (Use $$g = 9.8 \ \mathrm{m/s^2$})$$

$$v = \sqrt{2gh} = \sqrt{2 \times 9.8 \times 50} = 31.3 \ \mathrm{m/s}$$

Q: A 4 kg block moving at 20 m/s strikes a massless spring ($$k = 600 \ \mathrm{N/m}) on a $$frictionless surface. What is the maximum compression of the spring?

$$\Delta x = \sqrt{\frac{mv^2$}{k}} = \sqrt{\frac{4 \times 20^2$}{600}} = 1.63 \ \mathrm{m}$$

Q: A 30 kg block is connected to a 20 kg block on a smooth 53° incline. If released from rest, what is the speed of the system after the 30 kg block has descended 1 m? (Ignore friction, $$g = 9.8 \ \mathrm{m/s^2$})$$

$$v = \sqrt{\frac{2 \times 30 \times 9.8 \times 1 - 2 \times 20 \times 9.8 \times 1 \times \sin 53^\circ}{30 + 20}}$$

Question 1

Which of the following best describes the difference between conservative and non-conservative forces?

Accepted Answer

Conservative forces do not change the total mechanical energy of a system, while non-conservative forces can transform mechanical energy into other forms such as heat.

Question 2

A 2 kg ball is dropped from a height of 50 m. Ignoring air resistance, what is the speed of the ball just before it hits the ground? (Use $$g = 9.8 \ \mathrm{m/s^2$})$$

Accepted Answer

$$v = \sqrt{2gh} = \sqrt{2 	imes 9.8 	imes 50} = 31.3 \ \mathrm{m/s}$$

Question 3

Which equation correctly expresses the conservation of mechanical energy for a system with only conservative forces?

Accepted Answer

$$K_i + U_i = K_f + U_f$$

Question 4

A 4 kg block is attached to a spring with a spring constant $$k = 500 \ \mathrm{N/m}. If $$you push the block with a force of 100 N, what is the compression distance of the spring?

Accepted Answer

$$x = \frac{F}{k} = \frac{100}{500} = 0.2 \ \mathrm{m}$$

Question 5

A 0.5 kg hockey puck is moving at 4 m/s. You push it with a constant 200 N force over 0.3 m. What is the puck’s final speed? (Ignore friction)

Accepted Answer

$$v_f = \sqrt{v_i^2$ + \frac{2F d}{m}} = \sqrt{4^2$ + \frac{2 	imes 200 	imes 0.3}{0.5}} = 16 \ \mathrm{m/s}$$

Question 6

A 3 kg block hangs 2 m above the floor, connected to a 4 kg block on a rough table ($$\mu_k = 0.5). If $$released from rest, what is the speed of the 3 kg block just before hitting the floor? (Assume $$g = 9.8 \ \mathrm{m/s^2$})$$

Accepted Answer

$$v = \sqrt{2g h - 2 \mu_k m_2$ g h / (m_1$ + m_2$)}$$

Question 7

Which of the following statements about potential energy graphs is TRUE?

Accepted Answer

The force at any point is the negative of the slope of the potential energy graph at that point.

Question 8

A 4 kg block moving at 20 m/s strikes a massless spring ($$k = 600 \ \mathrm{N/m}) on a $$frictionless surface. What is the maximum compression of the spring?

Accepted Answer

$$\Delta x = \sqrt{\frac{mv^2$}{k}} = \sqrt{\frac{4 	imes 20^2$}{600}} = 1.63 \ \mathrm{m}$$

Question 9

Which of the following is a characteristic of a stable equilibrium point on a potential energy graph?

Accepted Answer

It is a local minimum of $$U(x)$$, and if displaced slightly, the object returns to equilibrium.

Question 10

A 2 kg object is dropped from 80 m and reaches the ground with 30 m/s. What is the work done by air resistance?

Accepted Answer

$$W_{air} = \Delta K + \Delta U = \frac{1}{2} m v^2$ - mgh = \frac{1}{2} 	imes 2 	imes 30^2$ - 2 	imes 9.8 	imes 80 = 900 - 1568 = -668 \ \mathrm{J}$$

Question 11

Which of the following is NOT a form of mechanical energy?

Accepted Answer

Thermal energy

Question 12

A 30 kg block is connected to a 20 kg block on a smooth 53° incline. If released from rest, what is the speed of the system after the 30 kg block has descended 1 m? (Ignore friction, $$g = 9.8 \ \mathrm{m/s^2$})$$

Accepted Answer

$$v = \sqrt{\frac{2 	imes 30 	imes 9.8 	imes 1 - 2 	imes 20 	imes 9.8 	imes 1 	imes \sin 53^\circ}{30 + 20}}$$

Question 13

Which of the following is TRUE about the work done by friction?

Accepted Answer

It is always negative, removing mechanical energy from the system.

Question 14

A ball is thrown from the top of a 30 m building with an initial speed of 20 m/s at an unknown angle. What is its speed just before hitting the ground? (Ignore air resistance, $$g = 9.8 \ \mathrm{m/s^2$})$$

Accepted Answer

$$v = \sqrt{v_0$^2 + 2gh} = \sqrt{20^2$ + 2 	imes 9.8 	imes 30} = 34.6 \ \mathrm{m/s}$$

Question 15

Which of the following is the correct expression for the elastic potential energy stored in a spring compressed by $$x$$ meters?

Accepted Answer

$$U_{el} = \frac{1}{2} k x^2$

Question 16

A particle moves according to the potential energy function $$U(x). At $$which points is the force on the particle zero?

Accepted Answer

Where the slope of $$U(x) is $$zero (horizontal tangent)

Potential Energy & Conservation – Study Notes (Young & Freedman University Physics, Ch 07)

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