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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