Work, Energy, and Power

Energy bookkeeping can replace a long force calculation. First decide which objects belong to the system, then track how energy enters, leaves, or changes form.

This lesson supports Chapter 7 of Physics for Beginners. Keep the physical picture in view, write the units, and check the direction of every vector before trusting a calculation.

Work transfers energy

For a constant force, work is \[W=Fd\cos\theta,\] where \(\theta\) is the angle between force and displacement. A force perpendicular to the motion does zero work. Positive work adds energy to a system, while negative work removes mechanical energy.

Kinetic and potential energy describe state

Kinetic energy is \(K=\tfrac12mv^2\). Near Earth’s surface, gravitational potential energy can be written \(U_g=mgh\). A spring stores \(U_s=\tfrac12kx^2\). If only conservative forces act, mechanical energy \(K+U\) stays constant.

Power tells how quickly energy changes

Average power is \[P=\frac{W}{\Delta t}=\frac{\Delta E}{\Delta t}.\] Two machines may do the same work, yet the one that finishes sooner delivers more power. The watt is one joule per second.

Worked example

A \(4\text{ kg}\) box is lifted \(2\text{ m}\) at steady speed. The increase in gravitational potential energy is \(mgh=4(9.8)(2)=78.4\text{ J}\). If the lift takes \(4\text{ s}\), the average power is \(78.4/4=19.6\text{ W}\).

Watch the idea in action

The Organic Chemistry Tutor gives a focused explanation of the chapter’s central idea. Pause before each calculation and predict the next step on paper.

Practice questions

1. Write the constant-force work formula.
2. What is the kinetic energy formula?
3. What is \(mgh\)?
4. When is mechanical energy conserved?
5. What does power measure?
6. How many joules per second are in one watt?

Answers

1. \(W=Fd\cos\theta\).
2. \(K=\tfrac12mv^2\).
3. Near-Earth gravitational potential energy.
4. When only conservative forces do work.
5. The rate of energy transfer or work.
6. One.

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