Work, Energy, and Power
Track how energy is transferred or transformed instead of memorizing isolated formulas.
Work, Energy, and Power
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Work transfers energy; power measures how fast
For a constant parallel force, W=Fd. Kinetic energy is ½mv², gravitational potential energy is mgh, and power is W/t. Energy changes form but is conserved in an isolated system.
Work–energy theorem
Net work equals the change in kinetic energy.
Power
Two machines may do equal work but have different power because their times differ.
Write the energy story first
Problem: A 2-kg ball moves at 4 m/s. Find its kinetic energy.
Recognize: Mass and speed are given, and speed must be squared.
Do it fast: KE=½(2)(4²)=16 J.
Why it works
Naming the initial and final energy forms reveals which quantities matter and reduces formula confusion.
Five forms you should recognize
Situation: A 20-N horizontal force moves a box 3 m in the same direction.
Why this is work: The force acts while the box moves in the force’s direction, so energy is transferred to the box.
Calculate: W = Fd = (20 N)(3 m) = 60 J.
Situation: A student holds a heavy bag motionless.
Why the answer is zero: The student exerts an upward force, but the bag does not move. Mechanical work on the bag requires displacement.
Calculate: W = Fd = F(0) = 0 J. The student may still feel tired because the body uses chemical energy internally.
Situation: A 2-kg ball moves at 4 m/s.
Why this formula applies: The energy comes from the ball’s motion, so use kinetic energy.
Calculate: KE = ½mv² = ½(2)(4²) = 16 J.
Notice: Because speed is squared, doubling the speed makes kinetic energy four times as large.
Situation: A 3-kg object is raised 5 m, using g ≈ 10 m/s².
Why this formula applies: Raising the object increases its energy because of its position in Earth’s gravitational field.
Calculate: GPE = mgh = (3)(10)(5) = 150 J. That energy can become kinetic energy if the object falls.
Situation: A machine does 600 J of work in 3 s.
Why time matters: Power does not measure how much work is done; it measures how quickly the work is done.
Calculate: P = W/t = 600 J ÷ 3 s = 200 W. A second machine doing the same work in less time would have greater power.
Check before you commit
- Forgetting the square in kinetic energy
- Using time in the work formula
- Calling force measured in joules
- Assuming energy is destroyed by friction
- Confusing work and power
- Allowing efficiency above 100%
Do you need the lesson-or just practice?
One original question in each form recommends your next step. It does not yet verify mastery.
Work at the level you need.
Foundations
Build the core procedure with immediate explanations.
Core Practice
Use mixed forms with less scaffolding.
UPCAT-Style Transfer
Apply the competency in unfamiliar representations.
Ready to verify this competency?
A score of 5/5 verifies mastery. An unsuccessful attempt loads a different five-form bank.
Work, Energy, and Power FAQ
Can a person feel tired while doing zero mechanical work?
Yes. Biology uses energy internally even if the object has no displacement.
Where does energy go with friction?
It is largely transferred to thermal energy and sometimes sound.
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