Q: A 2 kg object is dropped from a height of 10 m. Neglecting air resistance, what is its speed just before hitting the ground? Use $$g = 9.8 \ \mathrm{m/s^2$}.$$

$$v = \sqrt{2gh} = \sqrt{2 \times 9.8 \times 10} = \sqrt{196} = 14 \ \mathrm{m/s}$$

Q: A 5 kg mass is attached to a spring with $$k = 200 \ \mathrm{N/m}$$ and stretched 0.3 m from equilibrium. What is the elastic potential energy stored in the spring?

$$U_s = \frac{1}{2} \times 200 \times (0.3)^2$ = 9 \ \mathrm{J}$$

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

$$K = \frac{1}{2} m v^2$ = \frac{1}{2} \times 1 \times 16 = 8 \ \mathrm{J}$$

Question 1

Which of the following best describes the law of conservation of energy in a closed system?

Accepted Answer

Energy cannot be created or destroyed, only transferred or transformed within the system.

Question 2

A 2 kg object is dropped from a height of 10 m. Neglecting air resistance, what is its speed just before hitting the ground? Use $$g = 9.8 \ \mathrm{m/s^2$}.$$

Accepted Answer

$$v = \sqrt{2gh} = \sqrt{2 	imes 9.8 	imes 10} = \sqrt{196} = 14 \ \mathrm{m/s}$$

Question 3

Which equation correctly expresses the total mechanical energy $$E_{mech} of a $$system consisting of kinetic and potential energy?

Accepted Answer

$$E_{mech} = K + U$$

Question 4

A frictionless roller coaster starts from rest at height $$h_A$$ and descends to height $$h_C. $$What is the final speed $$v_f at $$the bottom, in terms of $$h_A$$ and $$h_C$$?

Accepted Answer

$$v_f = \sqrt{2g(h_A - h_C)}$$

Question 5

Which of the following is NOT a type of energy listed in the study materials?

Accepted Answer

Magnetic energy

Question 6

The potential energy stored in an ideal spring displaced by $$x$$ from equilibrium is given by:

Accepted Answer

$$U_s = \frac{1}{2}kx^2$

Question 7

If a system loses mechanical energy due to friction, which form of energy increases?

Accepted Answer

Thermal energy

Question 8

A 5 kg mass is attached to a spring with $$k = 200 \ \mathrm{N/m}$$ and stretched 0.3 m from equilibrium. What is the elastic potential energy stored in the spring?

Accepted Answer

$$U_s = \frac{1}{2} 	imes 200 	imes (0.3)^2$ = 9 \ \mathrm{J}$$

Question 9

Which statement about potential energy is correct according to the study materials?

Accepted Answer

Potential energy is a relative quantity, depending on the choice of reference point.

Question 10

A ball is thrown vertically upward with initial speed $$v_0. At $$its highest point, which of the following is true?

Accepted Answer

Kinetic energy is zero, potential energy is maximum.

Question 11

If the total mechanical energy of a system is constant, which of the following must be true?

Accepted Answer

No energy is transferred to or from the environment.

Question 12

A roller coaster car of mass $$m$$ starts from rest at height $$h_A$$ and descends to height $$h_C$$ with friction present. If its final speed is $$v_f$$, which equation best describes the energy lost to friction $$E_f$$?

Accepted Answer

$$E_f = m g (h_A - h_C) - \frac{1}{2} m v_f^2$

Question 13

Which of the following is a correct statement about equations of motion and conservation laws?

Accepted Answer

Equations of motion predict how a given physical quantity will change, while conservation laws describe quantities that remain constant.

Question 14

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

Accepted Answer

$$K = \frac{1}{2} m v^2$ = \frac{1}{2} 	imes 1 	imes 16 = 8 \ \mathrm{J}$$

Question 15

Which of the following scenarios best illustrates the conversion of potential energy to kinetic energy?

Accepted Answer

A compressed spring releasing and launching a ball.

Question 16

If a system consists of kinetic energy $$K$$, gravitational potential energy $$U_g$$, and elastic potential energy $$U_s$$, which equation represents the total mechanical energy?

Accepted Answer

$$E_{mech} = K + U_g + U_s$$

Question 17

A roller coaster car of mass 500 kg starts from rest at a height of 20 m and descends to a height of 5 m. What is its theoretical speed at the bottom, neglecting friction? ($$g = 9.8 \ \mathrm{m/s^2$})$$

Accepted Answer

$$v = \sqrt{2g(h_A - h_C)} = \sqrt{2 	imes 9.8 	imes 15} = \sqrt{294} \approx 17.1 \ \mathrm{m/s}$$

Question 18

Which of the following is a consequence of the conservation of mechanical energy in a frictionless system?

Accepted Answer

The sum of kinetic and potential energy remains constant.

Conservation of Energy: Principles, Types, and Applications

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