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 . Energy is the ability to do work, with key forms including kinetic energy , gravitational potential energy , and elastic potential energy . When only conservative forces act, total mechanical energy stays constant, so .
Power measures the rate of energy transfer, using or when force and velocity are in the same direction.
Key Facts
- Work is calculated by , where is the angle between the force and displacement.
- If force and displacement are in the same direction, work simplifies to because .
- If force is perpendicular to displacement, the work is because .
- Kinetic energy is energy of motion and is calculated by .
- Gravitational potential energy near Earth is calculated by , where is height above a chosen reference level.
- Elastic potential energy in a spring is calculated by .
- Conservation of mechanical energy is written as when friction and other nonconservative forces are ignored.
- Power is the rate of doing work or transferring energy, calculated by .
Vocabulary
- Work
- Work is energy transferred when a force causes displacement, calculated by .
- Kinetic Energy
- Kinetic energy is the energy an object has because of motion, calculated by .
- Potential Energy
- Potential energy is stored energy due to position or shape, such as or .
- Mechanical Energy
- Mechanical energy is the total of kinetic and potential energy, written as .
- Power
- Power is the rate at which work is done or energy is transferred, calculated by .
- Efficiency
- Efficiency compares useful output energy or work to input energy or work, calculated by .
Common Mistakes to Avoid
- Using the full force instead of the force component in the direction of motion is wrong because work depends on , not just .
- Forgetting that perpendicular forces do no work is wrong because when , .
- Using speed without squaring it in kinetic energy is wrong because the correct formula is , 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 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 force pulls a box across the floor in the same direction as the motion. What work is done?
- 2 A object moves at . What is its kinetic energy?
- 3 A motor does of work in . 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.
Understanding Work, Energy & Power
The direction of a force matters as much as its size. A person carrying a heavy backpack across a level hallway supports the backpack upward, while the backpack moves horizontally. The supporting force does no work on the backpack because it does not change the backpack's motion in that direction.
Friction is different. It acts opposite the motion, so it does negative work. Negative work means energy is removed from the moving object.
Brakes use this idea. Friction between brake pads and a wheel reduces the car's kinetic energy, mostly turning it into thermal energy.
In problems, draw force arrows and motion arrows before choosing a formula. This helps prevent using every force as if it transfers energy in the same way.
Potential energy depends on the system and on a chosen reference level. The floor is often called zero height, but it does not have to be. A shelf, a table, or the bottom of a ramp can be the reference.
Changing that choice changes the numerical value of gravitational potential energy, but it does not change the energy difference between two positions. Energy differences are what predict motion. A ball released from a high point speeds up because its gravitational potential energy decreases while its kinetic energy increases.
Speed has an especially strong effect on kinetic energy. Doubling an object's speed gives it four times as much kinetic energy. This is why stopping distance rises quickly at higher driving speeds.
Mechanical energy is not always conserved by itself. It remains constant only when forces such as friction and air resistance do not take energy out of the motion. In ordinary situations, total energy is still conserved, but some mechanical energy becomes thermal energy, sound, or energy in deformation.
A sliding box eventually stops because friction warms the box and the floor. The energy did not vanish. It became less useful for making the box move in one clear direction.
Good energy diagrams track where energy starts, where it ends, and which transfers occur. This method is often safer than trying to memorize a separate equation for every ramp, spring, or falling-object problem.
Power separates a slow energy transfer from a fast one. Two students may carry identical boxes up the same stairs, giving each box the same increase in gravitational potential energy. The student who finishes sooner produces more power.
This idea appears in light bulbs, engines, elevators, phone chargers, and household electricity use. A machine can make a task easier by changing the size or direction of a force, but it cannot create extra energy. A ramp reduces the force needed to raise an object, though the object must move farther along the ramp.
Real machines lose some input energy through friction, heating, vibration, and sound. Efficiency compares useful output energy or useful output work with the energy put in. When studying simple machines, identify the input, the useful output, and the losses before calculating anything.