Q: A 2 kg ball is dropped from a height of 5 m. Assuming no air resistance, what is the ball's speed just before it hits the ground? (Use $$g = 9.8\ \mathrm{m/s^2$})$$

$$v = \sqrt{2gh} = \sqrt{2 \times 9.8 \times 5} = 9.9\ \mathrm{m/s}$$

Q: A 0.5 kg mass is attached to a spring with spring constant $$k = 200\ \mathrm{N/m}$$ and is compressed by 0.1 m. What is the elastic potential energy stored in the spring?

$$U_s = \frac{1}{2}kx^2$ = \frac{1}{2} \times 200 \times (0.1)^2$ = 1\ \mathrm{J}$$

Q: A 1 kg object is moving at 4 m/s. What is its kinetic energy?

$$K = \frac{1}{2}mv^2$ = \frac{1}{2} \times 1 \times 4^2$ = 8\ \mathrm{J}$$

Q: A force of 10 N moves an object 3 m in the direction of the force. How much work is done?

$$W = Fd = 10 \times 3 = 30\ \mathrm{J}$$

Question 1

Which of the following best describes an isolated system in the context of energy conservation?

Accepted Answer

A system where only internal forces act and no energy is transferred into or out of the system by external forces.

Question 2

A 2 kg ball is dropped from a height of 5 m. Assuming no air resistance, what is the ball's speed just before it hits the ground? (Use $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$v = \sqrt{2gh} = \sqrt{2 	imes 9.8 	imes 5} = 9.9\ \mathrm{m/s}$$

Question 3

Which equation correctly expresses the law of conservation of energy for a system with thermal energy change?

Accepted Answer

$$K_f + U_f + \Delta E_{th} = K_i + U_i + W$$

Question 4

A block slides down a frictionless ramp. Which of the following statements is true about the energy transformations?

Accepted Answer

Gravitational potential energy is converted entirely into kinetic energy.

Question 5

A 0.5 kg mass is attached to a spring with spring constant $$k = 200\ \mathrm{N/m}$$ and is compressed by 0.1 m. What is the elastic potential energy stored in the spring?

Accepted Answer

$$U_s = \frac{1}{2}kx^2$ = \frac{1}{2} 	imes 200 	imes (0.1)^2$ = 1\ \mathrm{J}$$

Question 6

Which of the following best describes the turning point on a potential energy diagram?

Accepted Answer

It is where the total energy line crosses the potential energy curve and the object reverses direction.

Question 7

In the context of molecular bonds, what happens if the total energy line $$E is $$raised above the potential energy curve at the right side of the bond?

Accepted Answer

The molecular bond will break.

Question 8

Which of the following statements about chemical reactions and activation energy is correct?

Accepted Answer

A catalyst lowers the activation energy, increasing the reaction rate.

Question 9

A 1 kg object is moving at 4 m/s. What is its kinetic energy?

Accepted Answer

$$K = \frac{1}{2}mv^2$ = \frac{1}{2} 	imes 1 	imes 4^2$ = 8\ \mathrm{J}$$

Question 10

Which of the following is true for a perfectly elastic collision?

Accepted Answer

Both kinetic energy and momentum are conserved.

Question 11

A force of 10 N moves an object 3 m in the direction of the force. How much work is done?

Accepted Answer

$$W = Fd = 10 	imes 3 = 30\ \mathrm{J}$$

Question 12

Which of the following best describes the role of thermal energy in an inelastic collision?

Accepted Answer

Some mechanical energy is converted into thermal energy.

Question 13

A student runs up a 10 m high staircase in 8 seconds. If the student has a mass of 80 kg, what is the average power output? (Use $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$P = \frac{mgh}{t} = \frac{80 	imes 9.8 	imes 10}{8} = 980\ \mathrm{W}$$

Question 14

Which of the following is true about equilibrium positions on a potential energy diagram?

Accepted Answer

A local minimum in the potential energy curve corresponds to a stable equilibrium.

Question 15

A toy car of mass 200 g accelerates from rest to 2 m/s in 2 seconds. What is the average power output? (Ignore friction)

Accepted Answer

$$P = \frac{\Delta K}{t} = \frac{\frac{1}{2} 	imes 0.2 	imes 2^2$}{2} = \frac{0.4}{2} = 0.2\ \mathrm{W}$$

Question 16

Which of the following statements about the energy diagram of a spring-mass system is correct?

Accepted Answer

The potential energy curve is a parabola, and the total energy line is horizontal.

Question 17

In a chemical reaction, what does the activation energy represent?

Accepted Answer

The minimum energy required to break the bonds of the reactants.

Question 18

A block slides along a rough surface and comes to rest. Which energy transformation is primarily responsible for the block stopping?

Accepted Answer

Kinetic energy is converted into thermal energy due to friction.

Conservation of Energy and Energy Diagrams in Physics

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