Page 91 - Schaum's Outline of Theory and Problems of Applied Physics

76 ENERGY [CHAP. 7

SOLVED PROBLEM 7.7
The identical 65-kg twins Alpha and Beta climb a mountain 3800 m high. Alpha follows a trail that
◦
averages 20 above the horizontal, while Beta follows a different trail that averages 30 above the
◦
horizontal. How much work does each twin do?
In each case the height through which the twins raise their bodies is h = 3800 m. The exact route they follow
is irrelevant here. Hence each twin does the work
6
2
W = Fs = mgh = (65 kg)(9.8 m/s )(3800 m) = 2.42 × 10 J = 2.42 MJ
POWER
Power is the rate at which work is done by a force. Thus
W
P =
t
work done
Power =
time
The more power something has, the more work it can perform in a given time.
Two special units of power are in wide use, the SI watt and the British horsepower, where

1 watt (W) = 1 J/s = 1.34 × 10 −3 hp
1 horsepower (hp) = 550 ft·lb/s = 746 W
3
A kilowatt (kW) is equal to 10 W, or 1.34 hp. A kilowatthour is the work done in1hbyan agency whose power
6
output is 1 kW; hence 1 kWh = (1000 W)(3600 s) = 3.6 × 10 J.
When a constant force F does work on a body that is moving at the constant velocity v,if F is parallel to v
the power involved is
W Fs
P = =
t t
because s/t = v. That is,
P = Fv
Power = (force)(velocity)

EFFICIENCY

The efficiency, abbreviated Eff, of a system of some kind that takes power from a source and transmits it elsewhere
is given by the ratio between the power output of the system P out and its power input P in :

P out
Eff =
P in
An example of such a system is the winding drum of a hoist, which takes power from the rotating shaft of a
motor and delivers it through a linear pull on an object being raised.

SOLVED PROBLEM 7.8
A 40-kg woman runs up a staircase 4 m high in 5 s. Find her minimum power output.

The minimum downward force the woman’s legs must exert is equal to her weight mg. Hence
2
W Fs mgh (40 kg)(9.8 m/s )(4m)
P min = = = = = 314 W
t t t 5s