You are here
Run up the stairs in one minute or stroll up in five — the same work, but they feel completely different. That difference is power.
- Power is the rate at which work is done . Average power is the work done divided by the time taken: P = W t
- Doing more work in the same time, or the same work in less time, needs more power.
- The SI unit of power is the watt (W) : 1 W = 1 J s -1 (one joule of work per second).
- Power — the rate at which work is done; average power P = W / t.
- Watt (W) — the SI unit of power; 1 W = 1 joule of work done per second (1 J s⁻¹).
A weightlifter lifts a 75 kg mass by 2 m in 5 s. What power does she need? (g = 10 m s⁻²)
Work
= mgh
= 75 × 10 × 2
= 1500
J
.
P
=
W
t
=
1500
J
5
s
= 300
W
.
A 1000 kg car reaches 72 km h⁻¹ from rest in 10 s. Find the engine power needed.
v
= 72
km h
-1
= 20
m s
-1
,
u = 0
. Work
=
gain in KE
=
1
2
× 1000 × 20
2
= 200000
J
.
P
=
200000
J
10
s
= 20000
W
.
- The unit of power, the watt , is named in honour of James Watt , who invented an efficient steam engine that could generate rotational motion and move wheels.
- Another unit of power is horsepower (hp) , used for car engines and water pumps: 1 hp = 746 W . In the early days of engines, their power was compared with the power of actual horses that drove carriages.
NCERT Question 6 — A crane lifts a mass
A crane lifts a mass m to the 10th floor of a building in a certain time. It then raises the same mass to the 20th floor of the same building in double the time. How much more energy and power are required? Assume that the height of all floors is equal.
NCERT Question 7 — Which factors determine the energy
Which factors determine the energy required to raise a flag from the ground to the top of a tall flagpole using a pulley? Does raising the flag slowly or quickly change the amount of work done? If the speed at which the flag is raised is doubled, how does the power requirement change? Explain your answers.
-
Define power and give its SI unit.
Show Answer
Power is the rate at which work is done, P = W/t . Its SI unit is the watt (W), and 1 W = 1 J s⁻¹. -
Two students carry the same bag up the same stairs, one in 1 minute and one in 5 minutes. Who does more work, and who uses more power?
Show Answer
Both do the same work (same mgh). The faster one uses more power , because the same work is done in less time. -
How many watts is one horsepower?
Show Answer
1 horsepower = 746 W. -
A weightlifter lifts 75 kg by 2 m in 5 s. What power does she use? (g = 10 m s⁻²)
Show Answer
Work = mgh = 75 × 10 × 2 = 1500 J. Power = 1500 ÷ 5 = 300 W .
