Work, Energy & Power Cheat Sheet

A printable reference covering work, kinetic and potential energy, conservation of energy, power, efficiency, and simple machines for grades 9-11.

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Work, energy, and power explain how forces transfer energy and how fast that transfer happens. This cheat sheet helps students connect motion, height, speed, force, and time using the most common physics formulas. It is useful for solving problems involving lifting, pushing, falling, machines, and energy changes. Students need these ideas to understand motion in real systems and to prepare for algebra-based physics problems. Work is done when a force causes displacement in the direction of that force, using $W = Fd\cos\theta$ . Energy is the ability to do work, with key forms including kinetic energy $KE = \frac{1}{2}mv^2$ , gravitational potential energy $PE_g = mgh$ , and elastic potential energy $PE_s = \frac{1}{2}kx^2$ . When only conservative forces act, total mechanical energy stays constant, so $KE_i + PE_i = KE_f + PE_f$ . Power measures the rate of energy transfer, using $P = \frac{W}{t}$ or $P = Fv$ when force and velocity are in the same direction.

Key Facts

Work is calculated by $W = Fd\cos\theta$ , where $\theta$ is the angle between the force and displacement.
If force and displacement are in the same direction, work simplifies to $W = Fd$ because $\cos 0^{\circ} = 1$ .
If force is perpendicular to displacement, the work is $W = 0$ because $\cos 90^{\circ} = 0$ .
Kinetic energy is energy of motion and is calculated by $KE = \frac{1}{2}mv^2$ .
Gravitational potential energy near Earth is calculated by $PE_g = mgh$ , where $h$ is height above a chosen reference level.
Elastic potential energy in a spring is calculated by $PE_s = \frac{1}{2}kx^2$ .
Conservation of mechanical energy is written as $KE_i + PE_i = KE_f + PE_f$ when friction and other nonconservative forces are ignored.
Power is the rate of doing work or transferring energy, calculated by $P = \frac{W}{t} = \frac{\Delta E}{t}$ .

Vocabulary

Work: Work is energy transferred when a force causes displacement, calculated by $W = Fd\cos\theta$ .
Kinetic Energy: Kinetic energy is the energy an object has because of motion, calculated by $KE = \frac{1}{2}mv^2$ .
Potential Energy: Potential energy is stored energy due to position or shape, such as $PE_g = mgh$ or $PE_s = \frac{1}{2}kx^2$ .
Mechanical Energy: Mechanical energy is the total of kinetic and potential energy, written as $E_{mech} = KE + PE$ .
Power: Power is the rate at which work is done or energy is transferred, calculated by $P = \frac{W}{t}$ .
Efficiency: Efficiency compares useful output energy or work to input energy or work, calculated by $\text{efficiency} = \frac{E_{out}}{E_{in}} \times 100\%$ .

Common Mistakes to Avoid

Using the full force instead of the force component in the direction of motion is wrong because work depends on $F\cos\theta$ , not just $F$ .
Forgetting that perpendicular forces do no work is wrong because when $\theta = 90^{\circ}$ , $W = Fd\cos 90^{\circ} = 0$ .
Using speed without squaring it in kinetic energy is wrong because the correct formula is $KE = \frac{1}{2}mv^2$ , so doubling speed quadruples kinetic energy.
Applying conservation of mechanical energy when friction is significant is wrong because friction converts mechanical energy into thermal energy, so $KE_i + PE_i \ne KE_f + PE_f$ unless that energy loss is included.
Confusing work and power is wrong because work measures total energy transfer in joules, while power measures how quickly energy is transferred in watts.

Practice Questions

1 A $50\,\text{N}$ force pulls a box $4.0\,\text{m}$ across the floor in the same direction as the motion. What work is done?
2 A $2.0\,\text{kg}$ object moves at $6.0\,\text{m/s}$ . What is its kinetic energy?
3 A motor does $1200\,\text{J}$ of work in $8.0\,\text{s}$ . What is its power output?
4 A student carries a heavy backpack horizontally across a room at constant height. Explain whether the upward force from the student does work on the backpack.