Q: A ball of mass $$0.2\ \mathrm{kg} is $$dropped from a height of $$10\ \mathrm{m}$$ above the ground. Ignoring air resistance, what is the speed of the ball just before it hits the ground? (Take $$g = 9.8\ \mathrm{m/s^2$})$$

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

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

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

Q: A $$2\ \mathrm{kg}$$ block slides down a frictionless ramp from a height of $$5\ \mathrm{m}. $$What is its kinetic energy at the bottom of the ramp?

$$K = mgh = 2 \times 9.8 \times 5 = 98\ \mathrm{J}$$

Q: A $$0.3\ \mathrm{kg}$$ ball is thrown vertically upward with an initial speed of $$15\ \mathrm{m/s}. $$What is the maximum height reached by the ball? (Ignore air resistance, $$g = 9.8\ \mathrm{m/s^2$})$$

$$h = \frac{v_0$^2}{2g} = \frac{15^2$}{2 \times 9.8} = 11.5\ \mathrm{m}$$

Q: A $$1\ \mathrm{kg}$$ mass is attached to a spring ($$k = 100\ \mathrm{N/m}) $$and is compressed $$0.2\ \mathrm{m}$$ from equilibrium. If released from rest, what is its speed as it passes through equilibrium?

$$v = \sqrt{\frac{k}{m}}x = \sqrt{\frac{100}{1}} \times 0.2 = 2\ \mathrm{m/s}$$

Question 1

A ball of mass $$0.2\ \mathrm{kg} is $$dropped from a height of $$10\ \mathrm{m}$$ above the ground. Ignoring air resistance, what is the speed of the ball just before it hits the ground? (Take $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

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

Question 2

Which of the following statements best describes a conservative force?

Accepted Answer

A force for which the work done depends only on the initial and final positions, not on the path taken.

Question 3

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

Accepted Answer

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

Question 4

A projectile is launched from the ground with an initial speed $$v_0 at an $$angle $$	heta$$ above the horizontal. Ignoring air resistance, what is the speed of the projectile when it returns to the same vertical level from which it was launched?

Accepted Answer

$$v = v_0$

Question 5

A $$2\ \mathrm{kg}$$ block slides down a frictionless ramp from a height of $$5\ \mathrm{m}. $$What is its kinetic energy at the bottom of the ramp?

Accepted Answer

$$K = mgh = 2 	imes 9.8 	imes 5 = 98\ \mathrm{J}$$

Question 6

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

Accepted Answer

The work done by the force depends on the path taken.

Question 7

A block of mass $$m is $$attached to a spring and oscillates on a frictionless surface. If the block is released from rest at $$x = A$$, what is its speed as it passes through the equilibrium position ($$x = 0$$)?

Accepted Answer

$$v = \sqrt{\frac{k}{m}}A$$

Question 8

A parachutist falls at constant speed due to air resistance. Which statement is correct about the energy changes?

Accepted Answer

Gravitational potential energy decreases, and the work done by air resistance is negative.

Question 9

A $$0.3\ \mathrm{kg}$$ ball is thrown vertically upward with an initial speed of $$15\ \mathrm{m/s}. $$What is the maximum height reached by the ball? (Ignore air resistance, $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$h = \frac{v_0$^2}{2g} = \frac{15^2$}{2 	imes 9.8} = 11.5\ \mathrm{m}$$

Question 10

A block slides down a curved frictionless ramp from height $$h_1 to$$ $$h_2. $$Which of the following is true about the work done by gravity?

Accepted Answer

The work done by gravity depends only on $$h_1$$ and $$h_2$$, not on the path taken.

Question 11

A $$1\ \mathrm{kg}$$ mass is attached to a spring ($$k = 100\ \mathrm{N/m}) $$and is compressed $$0.2\ \mathrm{m}$$ from equilibrium. If released from rest, what is its speed as it passes through equilibrium?

Accepted Answer

$$v = \sqrt{\frac{k}{m}}x = \sqrt{\frac{100}{1}} 	imes 0.2 = 2\ \mathrm{m/s}$$

Question 12

Which of the following best describes the total mechanical energy of a system when only conservative forces are present?

Accepted Answer

It remains constant throughout the motion.

Question 13

A $$0.5\ \mathrm{kg}$$ mass is dropped from rest from a height of $$8\ \mathrm{m}$$ onto a spring with $$k = 400\ \mathrm{N/m}. $$What is the maximum compression of the spring? (Neglect air resistance and use $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$mgH = \frac{1}{2}kx^2$ \Rightarrow x = \sqrt{\frac{2mgH}{k}} = \sqrt{\frac{2 	imes 0.5 	imes 9.8 	imes 8}{400}} = 0.44\ \mathrm{m}$$

Question 14

Which of the following is a correct expression for the total potential energy in a system with both gravitational and elastic forces?

Accepted Answer

$$U = U_{grav} + U_{el}$$

Question 15

A $$0.2\ \mathrm{kg}$$ ball is thrown straight up with a speed of $$10\ \mathrm{m/s}. $$What is its kinetic energy when it reaches a height of $$3\ \mathrm{m}$$? ($$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$K = K_0$ - mg\Delta h = \frac{1}{2} 	imes 0.2 	imes 10^2$ - 0.2 	imes 9.8 	imes 3 = 10 - 5.88 = 4.12\ \mathrm{J}$$

Question 16

A block slides down a ramp and compresses a spring at the bottom. If the block starts from height $$h$$ and the spring constant is $$k$$, what is the maximum compression $$x of $$the spring?

Accepted Answer

$$mgh = \frac{1}{2}kx^2$ \Rightarrow x = \sqrt{\frac{2mgh}{k}}$$

Question 17

Which of the following is true about the elastic potential energy stored in a spring?

Accepted Answer

It is always non-negative and given by $$U_{el} = \frac{1}{2}kx^2$.

Potential Energy and Energy Conservation: Study Notes

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