Work, Energy and Power

Work, energy and power are three words used loosely in everyday speech and precisely here, and every question in the topic turns on one of the three precise meanings.

Work

Work = force x distance, where the distance is the distance moved in the direction of the force.

The unit is the joule. One joule is one newton acting over one meter.

A crate is pushed 5 meters with a force of 80 newtons. How much work is done?

80 times 5 is 400 joules.

If nothing moves, no work is done. Pushing against a wall that does not budge is zero work in the physics sense, no matter how hard you push or how tired you get. Holding a heavy box motionless is also zero work.

That is the definition questions are built on, because it conflicts with the everyday sense of the word.

Carrying a box horizontally is also zero work against gravity, because gravity acts downward and the motion is sideways. The distance has to be in the direction of the force.

Energy

Energy is the capacity to do work, and it is measured in joules, the same unit as work.

The two mechanical forms

Kinetic energy is energy of motion. It depends on mass and, more strongly, on speed: KE = one half x mass x velocity squared.

Because velocity is squared, doubling the speed gives four times the kinetic energy. That is why stopping distances grow so sharply with speed, and it is a question.

Potential energy is stored energy of position. Gravitational potential energy is PE = mass x gravity x height, so lifting something doubles its potential energy if you lift it twice as high.

Conservation

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Energy cannot be created or destroyed, only converted. This is the law of conservation of energy and it is the most asked idea in the topic.

The cart in the figure has all potential energy at the top and none at the bottom, and all kinetic at the bottom and none at the top, and the total is the same throughout. Nothing is lost; it changes form.

The same story in other systems:

When energy seems to disappear, it became heat. Friction is the usual culprit, and a question asking where the energy went in a real system wants that answer.

Other forms

Chemical, thermal, electrical, nuclear, sound, light and elastic energy are all forms the test may name. They convert into each other freely, which is what the conservation law permits.

Power

Power = work / time, and the unit is the watt. One watt is one joule per second.

Two workers each lift the same load to the same height. One takes 4 seconds and the other takes 8. Who does more work, and who supplies more power?

They do the same work - same force, same distance.

The faster one supplies twice the power, because power divides by time.

That question shape appears often and it is entirely about knowing that work and power are not the same quantity.

Horsepower is another unit of power, and one horsepower is about 746 watts.

Simple machines and efficiency

A machine does not create energy. It trades force for distance, which is the whole content of mechanical advantage.

Efficiency = useful energy out / energy in, expressed as a percentage.

No real machine is 100 percent efficient, because friction converts some of the input to heat. A question offering an efficiency above 100 percent is offering something impossible.

Moving in a circle

Centripetal force is the inward force that keeps something moving in a circle: the string on a whirled ball, gravity holding the Moon in orbit, friction holding a car on a curve. Let go of the string and the ball flies off in a straight line along the edge of the circle - not straight outward.

What you can skip

Across all 2,104 General Science questions in our bank:

• Horsepower and kilowatt conversions never appear on General Science. Power is asked in watts, as work divided by time.
• Efficiency calculations are rare (6 questions mention efficiency at all). Know that no machine is 100 percent efficient because some energy is always lost as heat.

Where people lose points

Saying work is done when nothing moves.

Saying energy is used up. It is converted.

Forgetting that kinetic energy depends on velocity squared.

Confusing work with power. Same work faster is more power.

Accepting an efficiency over 100 percent.

Using the wrong unit. Joules for work and energy, watts for power.

Work one in under a minute

A 2 kg ball is held 5 meters above the ground. Taking gravity as 10 m/s per second, what is its potential energy, and what is its kinetic energy just before it lands?

Potential energy: mass times gravity times height is 2 times 10 times 5, which is 100 joules.

Just before landing, all of that potential has become kinetic, so the kinetic energy is also 100 joules - ignoring air resistance.

The second half needed no formula at all, only the conservation law. That is usually true of these questions, and reaching for the kinetic energy formula is the slow route.

Where this leads

Mechanical advantage in Mechanical Comprehension is this lesson's force-for- distance trade, and the heat that friction produces is the next lesson.