Power

Power deals with the description of how quickly work is done or the time rate at which work is done or energy transferred.

Average power = Work done---------------Pav = W
--------------------time interval---------------------t

SCALE FOR POWER
1J/s = Watt
1hp = 550ftlb/s = 33000ftlb/min
1hp = 746W = 0.746kW
1kWh = 3.6 X 10^6 J = 3.6MJ

Formulas of POWER;
P = F.v----------------P = mav-------- P = mg(d / t)

P = F(d / t)----------------P = Wk / t

Sample Problem
1. A jet airplane engine develops a thrust ( a forward force on the plane) of 15,000N ( roughly 3000lb). When the plane is flying at 300m/s (roughly 600 mph), what horsepower does the engine develop?
P = F.v = (15000N) (300m/s) = 4.5X 10^6 W or 6030hp

2. As part of a charity fund-raising drive a Philippine marathon runner of mass 50.0kg runs up the stairs to the top of the Peninsula hotel, one of the tallest building in the Philippines (443m), in 15.0minutes.Find the average power output of the runner in watts, Kilowatts, and lastly in horsepower.

W = mgh = (50.0kg)(9.80m/s2)(443m) = 2.17 X 10^5 J

P = Wk / t = 2.17 X 105 J = 241 W or 0.241kW or 0.323hp
-------------------900s
Vave = d / t = 443m / 900s = 0.492 m/s

P = F.Vave = mg Vave = (50.0kg)(9.80m/s2)(0.492m/s) = 241 W

3. A boy with a mass 60kg walks up a flight of stairs 12m high in 30 seconds. What power has he used?
P = mg(d / t) = 60kg (10m/s^2)[(12m)/30s] = 240watts

4. A jet engine develops a thrust ( or forward force) of 1.5 X 10^4 N. When the plane is flying at 300m/s, what power in kilowatts is developed?
P = F.v = (15000N) (300m/s) = 4.5X 10^3 kW

5. A motor is rated at 20kW.At what speed in m/s can this motor raise a load weighing
2.5X 10^5N?

V = P / F

V= (20kW) (1000w/kW) = 2.0X10^4W = 0.8 X 10^-2m/s or 0.08m/s
------------------2.5X 10^5N--------2.5X 10^5N