Q: A block of mass $$m = 2\ \mathrm{kg}$$ slides down a ramp of height $$h = 1\ \mathrm{m}$$ and inclination $$\theta = 30^\circ. If $$its final speed is $$3.5\ \mathrm{m/s}$$, what is the coefficient of friction $$\mu on $$the ramp? (Use $$g = 9.8\ \mathrm{m/s^2$})$$

$$\mu = \frac{gh - \frac{1}{2}mv^2$}{mg \Delta x \cos \theta}$$

Q: If a projectile of mass $$m = 1\ \mathrm{kg} is $$launched horizontally with $$v_0 = 10$$\ \mathrm{m/s}$$ from a cliff of h = 3$$\ \mathrm{m}$$, but strikes the ground with speed 5$$\ \mathrm{m/s}$$, how much energy is lost to air resistance?

$$E_{\text{lost}} = 60.9\ \mathrm{J}$$

Q: A block of mass $$m$$ slides down a ramp of height $$h$$ and length $$\Delta x$$ with friction coefficient $$\mu. $$What is the work done by friction?

$$W_{fr} = \mu mg \Delta x \cos \theta$$

Question 1

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

Accepted Answer

A system where external forces or energy are transferred in or out, such as friction or air resistance.

Question 2

A projectile of mass $$m is $$launched horizontally with speed $$v_0$$ from a cliff of height $$h. $$What is the formula for its speed $$v$$ when it hits the ground, neglecting air resistance?

Accepted Answer

$$v = \sqrt{v_0$^2 + 2gh}$$

Question 3

If a projectile of mass $$m = 1\ \mathrm{kg} is $$launched horizontally with $$v_0 = 10$$\ \mathrm{m/s}$$ from a cliff of h = 3$$\ \mathrm{m}$$, what is its speed when it strikes the ground? (Use g = 9.8$$\ \mathrm{$$m/s^2$$}$$)

Accepted Answer

$$v = 12.6\ \mathrm{m/s}$$

Question 4

A projectile of mass $$m is $$launched from the ground at angle $$	heta$$ with speed $$v_0. $$What is its speed at the top of the arc (neglecting air resistance)?

Accepted Answer

$$v = v_0$ \cos 	heta$$

Question 5

A projectile is launched from the ground at angle $$	heta$$ with speed $$v_0. $$What is its speed when it returns to the ground (neglecting air resistance)?

Accepted Answer

$$v = v_0$

Question 6

A block of mass $$m = 2\ \mathrm{kg}$$ starts from rest and slides down a frictionless ramp of height $$h = 1\ \mathrm{m}. $$What is its speed at the bottom?

Accepted Answer

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

Question 7

A block of mass $$m = 2\ \mathrm{kg}$$ slides down a ramp of height $$h = 1\ \mathrm{m}$$ and inclination $$	heta = 30^\circ. If $$its final speed is $$3.5\ \mathrm{m/s}$$, what is the coefficient of friction $$\mu on $$the ramp? (Use $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$\mu = \frac{gh - \frac{1}{2}mv^2$}{mg \Delta x \cos 	heta}$$

Question 8

If a projectile of mass $$m = 1\ \mathrm{kg} is $$launched horizontally with $$v_0 = 10$$\ \mathrm{m/s}$$ from a cliff of h = 3$$\ \mathrm{m}$$, but strikes the ground with speed 5$$\ \mathrm{m/s}$$, how much energy is lost to air resistance?

Accepted Answer

$$E_{	ext{lost}} = 60.9\ \mathrm{J}$$

Question 9

Which of the following is NOT a form of energy considered in the conservation of energy problems discussed?

Accepted Answer

Thermal Energy

Question 10

In a closed system, which of the following statements is true regarding energy transfer?

Accepted Answer

No external forces or energy are transferred in or out of the system.

Question 11

A block slides down a ramp with friction. Which term accounts for the energy lost due to friction?

Accepted Answer

$$W_{NC}$$

Question 12

Which equation correctly represents the conservation of energy for a system with non-conservative work?

Accepted Answer

$$KE_1$$ + $$PE_1 + W$$_{NC} = $$KE_2$$ + $$PE_2$$

Question 13

A block of mass $$m$$ slides down a ramp of height $$h$$ and length $$\Delta x$$ with friction coefficient $$\mu. $$What is the work done by friction?

Accepted Answer

$$W_{fr} = \mu mg \Delta x \cos 	heta$$

Question 14

Which of the following is a correct step in energy problem solving according to the lecture?

Accepted Answer

Identify the objects in your system and whether it is open or closed.

Question 15

A projectile is launched horizontally from a height $$h$$ with initial speed $$v_0. If $$air resistance is present, which of the following is true about its final speed when it hits the ground?

Accepted Answer

It will be less than $$\sqrt{v_0$^2 + 2gh}.$$

Question 16

Which of the following is a plausible reason for energy loss in a real-world projectile motion scenario?

Accepted Answer

Air resistance

Question 17

If a block slides down a ramp and its final kinetic energy is less than its initial potential energy, what can be inferred?

Accepted Answer

Some energy was lost to non-conservative forces such as friction.

Question 18

Which of the following is NOT a step in the energy problem-solving method outlined in the lecture?

Accepted Answer

Ignore external energy transfers.

Question 19

A block of mass $$m$$ slides down a ramp of height $$h$$ and length $$\Delta x$$ with friction coefficient $$\mu. $$Which equation gives the coefficient of friction if the final speed is $$v$$?

Accepted Answer

$$\mu = \frac{gh - \frac{1}{2}v^2$}{g \Delta x \cos 	heta}$$

Conservation of Energy & Problem Solving in Physics

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