Mechanical ComprehensionLesson 2 of 18
Work, Energy and Power
Work as force times distance, kinetic and potential energy, and power as work over time.
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General Science defines these three. This lesson uses them, because in Mechanical Comprehension they are how you check whether an answer about a machine is possible at all.
Work
Work = force x distance moved in the direction of the force.
Units are foot-pounds, inch-pounds or joules.
A 40-pound crate is pushed 12 feet.
40 times 12 is 480 foot-pounds.
No movement, no work. Holding a load steady is zero work in this sense, however hard it is, and pushing against something immovable is zero work too.
Carrying a load horizontally does no work against gravity, because gravity acts downward and the motion is sideways.
Work is the check
This is the practical point of the lesson.
Every machine leaves work unchanged - less friction, which only reduces the output. So for any machine question:
Work in = force in x distance in. Work out = force out x distance out. They must match.
A pulley system lifts 800 pounds by 2 feet using 200 pounds of effort. How much rope is pulled?
Work out: 800 times 2 is 1,600 foot-pounds.
Work in must equal it: 1,600 divided by 200 is 8 feet of rope.
That single equation answers most machine questions without knowing which machine it is. It works for levers, pulleys, ramps, gears and jacks indifferently.
And it rules out impossible answers immediately. Any choice implying more work out than in is wrong.
Energy
Energy is the capacity to do work, in the same units.
Potential energy is stored by position - a raised load, a compressed spring, a drawn bow.
Kinetic energy is energy of motion.
They convert into each other and the total is constant, which is what the figure shows. A falling object trades potential for kinetic; a flywheel spinning up stores kinetic energy and gives it back.
Kinetic energy depends on the square of the speed, so doubling a vehicle's speed quadruples the energy its brakes must remove. That is the most practical consequence and it is asked.
Power
Power = work / time. Units are foot-pounds per second, watts or horsepower.
One horsepower is 550 foot-pounds per second, or about 746 watts.
A hoist lifts 1,000 pounds 10 feet in 20 seconds.
Work: 10,000 foot-pounds. Power: 10,000 divided by 20 is 500 foot-pounds per second, which is a little under 1 horsepower.
Doing a job faster requires more power and the same work. Two hoists lifting identical loads to the same height do identical work; the quicker one is more powerful.
A more powerful machine does not do more work. It does the same work sooner. That distinction is a question, and it is the one people get wrong.
A machine with a large mechanical advantage is not more powerful. A hand jack can lift a car with a small effort, and it is very slow, so its power is low. Force, work and power are three different quantities, and a question comparing two machines is usually asking which one you have actually been given.
Efficiency
Efficiency = work out / work in, as a percentage.
No machine reaches 100 percent, because friction converts part of the input to heat.
A machine receives 500 foot-pounds and delivers 400.
400 over 500 is 80 percent, and the missing 100 foot-pounds became heat.
The lost energy is not destroyed. It left as heat, which is the answer to "where did the rest of the energy go".
The pendulum
A pendulum trades potential energy for kinetic energy on every swing. At the highest point it stops for an instant, so its energy is all potential; at the lowest point it moves fastest, so its energy is all kinetic. Without friction the total stays constant - the energy only changes form.
What you can skip
Across the 137 questions on this topic in our bank:
- Metric energy units. Joules come up three times and kilowatts twice; the calculations use foot-pounds and horsepower.
- Energy in other forms. The questions stay with mechanical work, kinetic and potential energy, power and efficiency.
Where people lose points
Counting work when nothing moved.
Thinking a machine reduces the work needed. It reduces force and increases distance.
Confusing power with work or with force.
Forgetting kinetic energy goes with speed squared.
Saying lost energy disappeared. It became heat.
Accepting an efficiency above 100 percent.
Work one in under a minute
A ramp is used to load a 900-pound crate onto a truck bed 4 feet high. The ramp is 16 feet long. How much work is done, and what force is needed?
Work is set by the load and the height, not by the ramp: 900 times 4 is 3,600 foot-pounds. The ramp does not change it.
Force: the same work over 16 feet means 3,600 divided by 16, which is 225 pounds.
Check against the advantage: 16 over 4 is 4, and 900 divided by 4 is 225. Agreed.
Notice which quantity the ramp changed and which it did not. That is the lesson.
Where this leads
The work check applies to every machine in this subtest, and the energy lost to friction is the subject of the next lesson.
Related lessonsReference
- Mechanical Advantage - the trade the work check verifies
- Friction - where the missing energy goes
- Momentum and Collisions - the other conserved quantity
- Work, Energy and Power - the same three defined rather than applied
Practice this topic
Check that this lesson stuck. Answer questions on work, energy and power only, and see the right answer and why after each one.
Practice Work, Energy and Power questions