Q: A 2 kg object is attached to a horizontal spring with spring constant $$k = 200\ \mathrm{N/m}. $$The spring is compressed by $$0.1\ \mathrm{m}$$ from equilibrium and released from rest. What is the object's speed as it passes through equilibrium?

$$v = \sqrt{\dfrac{k (\Delta x)^2$}{m}} = \sqrt{\dfrac{200 \times (0.1)^2$}{2}} = 1\ \mathrm{m/s}$$

Q: A 5 kg watermelon is dropped from a height of 11 m and falls into a 3 m deep hole. What is its speed when it hits the bottom? (Neglect air resistance, $$g = 9.8\ \mathrm{m/s^2$}.)$$

$$v = \sqrt{2g(11 + 3)} = \sqrt{2 \times 9.8 \times 14} = 16.6\ \mathrm{m/s}$$

Q: A pendulum of length $$0.78\ \mathrm{m} is $$released from rest at $$60^\circ$$ from the vertical. What is the speed of the $$0.15\ \mathrm{kg}$$ mass at the lowest point? ($$g = 9.8\ \mathrm{m/s^2$})$$

$$v = \sqrt{2gL(1 - \cos\theta)} = \sqrt{2 \times 9.8 \times 0.78 \times (1 - \cos 60^\circ)} = 3.5\ \mathrm{m/s}$$

Question 1

A 0.5 kg ball is thrown vertically upward with an initial speed of 10 m/s. Neglecting air resistance, what is the maximum height the ball reaches above its starting point? (Use $$g = 9.8\ \mathrm{m/s^2$}.)$$

Accepted Answer

$$h = \dfrac{v_0$^2}{2g} = \dfrac{100}{19.6} = 5.1\ \mathrm{m}$$

Question 2

Which of the following statements about potential energy is CORRECT?

Accepted Answer

Potential energy is only associated with conservative forces, for which the work done is independent of the path.

Question 3

A block of mass $$m$$ slides down a frictionless curved ramp from height $$h. $$Which of the following is TRUE about the block's speed at the bottom?

Accepted Answer

The speed depends only on the vertical height $$h$$ and not on the path taken.

Question 4

A 2 kg object is attached to a horizontal spring with spring constant $$k = 200\ \mathrm{N/m}. $$The spring is compressed by $$0.1\ \mathrm{m}$$ from equilibrium and released from rest. What is the object's speed as it passes through equilibrium?

Accepted Answer

$$v = \sqrt{\dfrac{k (\Delta x)^2$}{m}} = \sqrt{\dfrac{200 	imes (0.1)^2$}{2}} = 1\ \mathrm{m/s}$$

Question 5

A 5 kg watermelon is dropped from a height of 11 m and falls into a 3 m deep hole. What is its speed when it hits the bottom? (Neglect air resistance, $$g = 9.8\ \mathrm{m/s^2$}.)$$

Accepted Answer

$$v = \sqrt{2g(11 + 3)} = \sqrt{2 	imes 9.8 	imes 14} = 16.6\ \mathrm{m/s}$$

Question 6

Which of the following best describes the relationship between force and potential energy for a conservative force?

Accepted Answer

The force is the negative of the derivative of the potential energy with respect to position: $$F = -\dfrac{dU}{dx}.$$

Question 7

A pendulum of length $$0.78\ \mathrm{m} is $$released from rest at $$60^\circ$$ from the vertical. What is the speed of the $$0.15\ \mathrm{kg}$$ mass at the lowest point? ($$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$v = \sqrt{2gL(1 - \cos	heta)} = \sqrt{2 	imes 9.8 	imes 0.78 	imes (1 - \cos 60^\circ)} = 3.5\ \mathrm{m/s}$$

Question 8

Which of the following is NOT a characteristic of a conservative force?

Accepted Answer

The force always increases the system's thermal energy.

Question 9

A block of mass $$m is $$placed on top of a vertical spring (spring constant $$k) $$and compresses it by $$\Delta y at $$equilibrium. What is the value of $$\Delta y$$?

Accepted Answer

$$\Delta y = \dfrac{mg}{k}$$

Question 10

A mountain climber drags a bag of supplies up a slope at constant speed. The tension in the rope is an external force. Which energy changes occur in the system (earth + bag + slope)?

Accepted Answer

Potential energy increases and thermal energy increases due to friction.

Question 11

Which of the following statements about energy bar charts is correct?

Accepted Answer

They are used to visualize energy conservation and transformations within a system.

Question 12

A particle moves in a potential energy curve with a minimum at $$x = x_0$. What type of equilibrium is this?

Accepted Answer

Stable equilibrium

Question 13

A 0.025 kg pebble is shot straight up at 17 m/s. Ignoring air resistance, what is the maximum height reached? ($$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$h = \dfrac{v_0$^2}{2g} = \dfrac{289}{19.6} = 14.7\ \mathrm{m}$$

Question 14

Which of the following is TRUE regarding the zero of potential energy?

Accepted Answer

Only changes in potential energy $$\Delta U$$ have physical significance.

Question 15

A block slides down a rough incline, losing mechanical energy due to friction. Which statement is correct?

Accepted Answer

Some mechanical energy is transformed into thermal energy.

Question 16

A particle is released from rest at position $$x_1 on a $$potential energy curve. At which position will it have maximum speed?

Accepted Answer

At the position where the potential energy is minimum.

Question 17

Which of the following is NOT a nonconservative force?

Accepted Answer

Gravity

Question 18

The work done by gravity on an object moving from height $$y_i to$$ $$y_f is$$:

Accepted Answer

$$W = -mg(y_f - y_i)$$

Question 19

A mass attached to a spring oscillates horizontally on a frictionless surface. Which statement is correct about the energy transformations?

Accepted Answer

Kinetic energy is transformed into elastic potential energy and vice versa, with total mechanical energy conserved.

Chapter 10: Interactions and Potential Energy – Study Notes

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