# Work, Energy, and Power

Computer Science I · Physics · https://tryals.app/learn/computer-science-i/work-energy-and-power

## The Currency of Physics

**Energy** is the universal capacity to do work, and **work** is the transfer of energy by a force: $W = Fd\cos\theta$. Work is measured in **joules**.

| Mechanical Form | Formula | Key Detail |
| --- | --- | --- |
| **Kinetic Energy** | $KE = \frac{1}{2}mv^2$ | Speed is squared; doubling $v$ quadruples $KE$. |
| **Potential Energy** | $PE = mgh$ | Stored energy of position near Earth. |

A force perpendicular to motion does **no** work. Friction converts mechanical energy into heat, making real systems seem to lose energy.

## Conservation and Power

The **work-energy theorem** states that net work equals the change in kinetic energy. In an isolated system without friction, total mechanical energy ($KE + PE$) remains **constant**.

**Power** is the rate of doing work: $P = \frac{W}{t}$, measured in **watts**. Two engines can do the same work, but the more powerful one finishes faster.

> **Common pitfall:** Confusing **energy** (total work capacity) with **power** (the rate of transfer). A low-power device can deliver high total energy given enough time.

## Practice questions

4 of this lesson's 9 practice questions, with answers. The full set is in the app.

### 1. A ball is dropped from a height in the absence of air resistance. Select every statement that is TRUE during the fall.

A. Energy is created as it speeds up
B. Its kinetic energy grows in proportion to the square of its speed
C. Nothing is gained or lost overall: the two forms simply trade
D. Its potential energy decreases
E. Its kinetic energy increases

**Answer:** B. Its kinetic energy grows in proportion to the square of its speed; C. Nothing is gained or lost overall: the two forms simply trade; D. Its potential energy decreases; E. Its kinetic energy increases

**Why:** Height is traded for speed, so potential energy falls while kinetic energy rises by exactly the same amount and the total is unchanged. Nothing is created: the energy was already there, stored by the work done in lifting the ball.

Page: https://tryals.app/practice/computer-science-i/work-energy-and-power/a-ball-is-dropped-from-a-height-in-the-absence-of-air-resistance

### 2. Work and energy share the joule while power takes the watt. What does that difference in units record?

A. That watts measure force rather than energy
B. That power applies to electrical systems and energy to mechanical ones
C. That power is the total energy available and energy is what is used
D. That power is energy per unit time, so it is a rate

**Answer:** D. That power is energy per unit time, so it is a rate

**Why:** A rate and an amount are different quantities. This is why an engine is rated in watts and a battery in joules, one is how fast, the other is how much.

Page: https://tryals.app/practice/computer-science-i/work-energy-and-power/work-and-energy-share-the-joule-while-power-takes-the-watt-what-does

### 3. A ball dropped from a given height arrives at the ground with a speed that does not depend on its mass.

**Answer:** True

**Why:** True. $mgh = \tfrac12 mv^{2}$ gives $v = \sqrt{2gh}$, the mass cancels. That is Galileo's result, and it holds only while air resistance is negligible: a feather and a hammer fall together on the Moon and visibly do not on Earth, because drag depends on shape and area rather than mass.

Page: https://tryals.app/practice/computer-science-i/work-energy-and-power/a-ball-dropped-from-a-given-height-arrives-at-the-ground-with-a-speed

### 4. A regenerative braking system recovers perhaps 70% of a vehicle's kinetic energy, never 100%. Which law sets the ceiling?

A. The first law, since energy is destroyed during braking
B. None, 100% recovery is achievable with better engineering
C. The second law, since every conversion disperses some heat
D. Conservation of momentum, which limits the transferable energy

**Answer:** C. The second law, since every conversion disperses some heat

**Why:** No energy is destroyed, the first law forbids that, and some is converted to heat spread across the motor, wiring and air, which cannot be reassembled into motion without further loss. Efficiency is bounded by the second law, so 70% is close to the practical ceiling rather than a failure of engineering.

Page: https://tryals.app/practice/computer-science-i/work-energy-and-power/a-regenerative-braking-system-recovers-perhaps-70-of-a-vehicles