Power
- Define power as the rate of doing work, P = W/t
- Relate power to force and velocity, P = Fv
- Compare machines by how quickly they deliver energy
Power is how fast work gets done
Power is the rate at which work is done or energy is transferred, P = W/t, measured in watts (W) — one watt is one joule per second. Two motors that lift the same load the same height do the same work, but the one that does it faster has more power. Power is why a sports car and an economy car can both reach the top of a hill, yet one gets there far sooner.
Power from force and speed
When a constant force pushes an object moving at speed v, the power delivered is P = Fv. This form is handy because it needs no clock: a locomotive pulling with force F at cruising speed v delivers power Fv continuously. It also explains why a car needs far more power to maintain high speed — at greater v, the same drag force demands more power to overcome.
A motor lifts a load, doing 600 J of work in 3 s. Then it pulls a sled with a steady 50 N force at 4 m/s. Find the power in each case.
- 1.Lifting: P = W/t = 600 J ÷ 3 s = 200 W.
- 2.Pulling: the force is constant and along the motion, so use P = Fv.
- 3.Compute: P = 50 N × 4 m/s = 200 W.
- 4.Both tasks deliver the same power, 200 W, by two different routes.
Pick the power formula that matches your givens. Total work and a time interval → P = W/t. A steady force and a speed → P = Fv. Both give watts; they are just two views of the same rate.
A crane does 5000 J of work in 10 s. What is its power output?
A motor exerts a steady 100 N force to move a load at a constant 5 m/s. What power does it deliver?
Remember that power and energy are different quantities: energy (joules) is the total transferred, power (watts) is the rate. A question asking "how quickly" or "per second" is about power; "how much total" is about energy or work.
Answer the 2 checkpoints as you read.
Sign in to save your progress