Work, Energy, and Power
Work and Energy
Work done by a force
Work is the transfer of energy by a force acting through a displacement. For a constant force, . More generally, .
If a force is perpendicular to displacement, what is the work done?
When the force is perpendicular to displacement, , so the work is zero.
Correct answer: Zero
State the work-energy theorem.
The theorem is , linking forces directly to speed changes.
Correct answer: Net work equals change in kinetic energy
Conservation of Energy
Mechanical energy
When only conservative forces act, mechanical energy is conserved. Common potentials include gravitational potential energy near Earth and spring potential energy .
Problem-solving strategy
If forces are complicated but energy changes are simple, energy methods can be faster than Newton’s laws.
Energy and power relations
| Quantity | Formula | Meaning |
|---|---|---|
| Kinetic energy | Energy of motion | |
| Gravitational potential | Energy due to height | |
| Spring potential | Stored elastic energy | |
| Power | Rate of energy transfer |
Which expression gives power?
Power is the rate at which work is done or energy is transferred, so .
Correct answer:
Why is power important in engineering systems?
Power determines whether a motor, battery, or engine can sustain a required load.
Correct answer: It indicates how fast energy is delivered or used
Design insight
Two devices may do the same work, but the one that completes it faster requires greater power.