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

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

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

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

Question 1

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

Accepted Answer

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

Question 2

Which of the following is a non-conservative force?

Accepted Answer

Friction

Question 3

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

Accepted Answer

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

Question 4

Which equation correctly expresses the conservation of mechanical energy for a falling object (ignoring air resistance)?

Accepted Answer

$$K_i + U_{g,i} = K_f + U_{g,f}$$

Question 5

A 0.5 kg hockey puck is moving at $$4 \ \mathrm{m/s} on $$frictionless ice. You push it with a constant $$200 \ \mathrm{N}$$ force over $$0.3 \ \mathrm{m}. $$What is its final speed?

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 2-kg object is dropped from $$80 \ \mathrm{m}$$ and hits the ground at $$30 \ \mathrm{m/s}. $$What is the work done by air resistance?

Accepted Answer

$$W_{air} = \Delta K + \Delta U = \frac{1}{2} m v_f^2$ - mgh = \frac{1}{2} 	imes 2 	imes 30^2$ - 2 	imes 9.8 	imes 80 = -784 \ \mathrm{J}$$

Question 7

Which of the following statements about conservative forces is TRUE?

Accepted Answer

Work done by a conservative force is path-independent.

Question 8

A rollercoaster cart must complete a vertical loop of radius $$R. $$What is the minimum speed at the top of the loop to avoid falling?

Accepted Answer

$$v_{min} = \sqrt{gR}$$

Question 9

A 3-kg block hangs 2 m above the floor, connected by a pulley 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?

Accepted Answer

$$v = \sqrt{\frac{2(m_1$ g h - f_k d)}{m_1$ + m_2$}}$$

Question 10

Which of the following best describes the energy transformation when a block slides to a stop due to friction?

Accepted Answer

Kinetic energy is transformed into thermal energy.

Question 11

A pendulum is released from a height $$h$$ above its lowest point. What is its maximum speed at the bottom?

Accepted Answer

$$v_{max} = \sqrt{2gh}$$

Question 12

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

Accepted Answer

Where $$\frac{dU}{dx} = 0$$

Question 13

A 4-kg block is pushed against a spring ($$k = 500 \ \mathrm{N/m}) $$with a force of $$100 \ \mathrm{N}. $$What is the compression distance $$x$$?

Accepted Answer

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

Question 14

Which of the following is TRUE about potential energy graphs $$U(x)$$?

Accepted Answer

Stable equilibrium occurs at a local minimum of $$U(x).$$

Question 15

A 6-kg object is thrown downward from a height of $$20 \ \mathrm{m}$$ and hits the ground at $$30 \ \mathrm{m/s}. $$What was its initial speed?

Accepted Answer

$$v_0$$ = \sqrt{v_$$f^2 - 2gh$$} = \sqrt{$$30^2 - 2$$ 	imes 9.8 	imes 20} = 10 \ \mathrm{m/s}$$

Question 16

A block slides on a rough surface with initial speed $$v_0 = 30$$ \ \mathrm{m/s}$$ and coefficient of friction $$\mu = 0.6$$. How far does it travel before stopping?

Accepted Answer

$$d = \frac{v_0$^2}{2 \mu g}$$

Question 17

A 0.1 kg particle moves according to the potential energy graph $$U(x). $$What is the minimum speed needed at point A to reach point B if $$U_A = 2 \ \mathrm{J}$$ and $$U_B = 8 \ \mathrm{J}$$?

Accepted Answer

$$v_{min} = \sqrt{\frac{2(U_B - U_A)}{m}} = \sqrt{\frac{2 	imes (8-2)}{0.1}} = 10.95 \ \mathrm{m/s}$$

Conservation of Energy in Physics: Concepts, Applications, and Problem Solving

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