Question 1

A block of mass $$m is $$released from rest at the top of a frictionless incline of height $$h. $$What is its speed at the bottom of the incline?

Accepted Answer

$$v = \sqrt{2gh}$$

Question 2

Which of the following correctly expresses the work-energy theorem as shown in the notes?

Accepted Answer

$$\Delta U = -W_{	ext{INT}}$$

Question 3

A 2 kg mass is released from rest at the top of a 5 m long incline at $$30^\circ to $$the horizontal. The coefficient of kinetic friction is $$\mu_k = 0.1. $$What is the final speed of the mass at the bottom of the incline? (Use $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$v_f = 6.3\ \mathrm{m/s}$$

Question 4

The gravitational potential energy near the surface of the Earth is given by which of the following expressions?

Accepted Answer

$$U_g(y) = mgy$$

Question 5

A spring with $$k = 100\ \mathrm{N/m} is $$compressed by $$0.5\ \mathrm{m}. A$$ $$0.5\ \mathrm{kg}$$ mass is placed against the spring and released up a $$5\ \mathrm{m}$$ ramp inclined at $$15^\circ. $$How far from the end of the ramp does the mass land? (Assume no friction and $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$\Delta x = 3.25\ \mathrm{m}$$

Question 6

For a system with only conservative forces and no external work, which of the following is true?

Accepted Answer

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

Question 7

A rollercoaster car of mass $$m$$ starts from rest at height $$h$$ and must complete a vertical loop of radius $$R. $$What is the minimum height $$h$$ required for the car to just make it around the loop (neglecting friction)?

Accepted Answer

$$h = \frac{5}{2}R$$

Question 8

Which of the following best describes the change in elastic potential energy for a spring compressed from $$\Delta s_i to$$ $$\Delta s_f$$?

Accepted Answer

$$\Delta U_{sp} = \frac{1}{2}k(\Delta s_f^2$ - \Delta s_i^2$)$$

Question 9

A mass $$m is $$attached to a frictionless spring of constant $$k$$ and released from rest at a displacement $$A$$ from equilibrium. What is the maximum speed of the mass?

Accepted Answer

$$v_{max} = A\sqrt{\frac{k}{m}}$$

Question 10

In the context of energy conservation, what does $$\Delta E_{th}$$ represent?

Accepted Answer

The change in thermal energy due to dissipative forces like friction

Question 11

A $$0.5\ \mathrm{kg}$$ mass is launched by a spring (compressed $$0.5\ \mathrm{m}$$, $$k = 100\ \mathrm{N/m}) up a$$ $$5\ \mathrm{m}$$ ramp at $$15^\circ. $$What is the launch speed $$v_L of $$the mass as it leaves the spring? (Assume $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$v_L = 4.95\ \mathrm{m/s}$$

Question 12

If a block slides down a rough incline, which term accounts for the energy lost due to friction?

Accepted Answer

$$\Delta E_{th}$$

Question 13

Which of the following is the correct expression for the work done by a spring on a mass as it moves from $$\Delta s_i to$$ $$\Delta s_f$$?

Accepted Answer

$$W_{M} = -\frac{k}{2}[(\Delta s_f)^2$ - (\Delta s_i)^2$]$$

Question 14

A mass $$m is $$released from rest at height $$y_i$$ and falls to $$y_f. $$What is the change in gravitational potential energy?

Accepted Answer

$$\Delta U_g = mg(y_f - y_i)$$

Question 15

In the energy conservation equation $$K_i + U_{sp,i} + U_{g,i} = K_f + U_{sp,f} + U_{g,f} + \Delta E_{th}$$, what does $$\Delta E_{th}$$ represent in a real-world scenario?

Accepted Answer

Energy lost to friction or air resistance

Question 16

A mass is attached to a spring and oscillates on a frictionless surface. If the spring is compressed by $$A$$ and released, what is the total mechanical energy of the system?

Accepted Answer

$$E_{mech} = \frac{1}{2}kA^2$

Question 17

Which of the following is NOT a correct statement about mechanical energy conservation?

Accepted Answer

Mechanical energy is always conserved, even in the presence of friction.

Work, Energy, and Conservation Principles in Mechanics

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