Page 92 - Schaum's Outline of Theory and Problems of Applied Physics

CHAP. 7] ENERGY 77

SOLVED PROBLEM 7.9
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A man uses a horizontal force of 200 N to push a crate up a ramp 8 m long that is 20 above the horizontal.
(a) How much work does the man perform? (b) If the man takes 12 s to push the crate up the ramp, what
is his power output in watts and in horsepower?

◦
(a) W = Fs cos θ = (200 N)(8m)(cos 20 ) = 1504 J
W 1504 J
(b) P = = = 125 W
t 12 s
Since 1 hp = 746 W,

125 W
P = = 0.17 hp
746 W/hp

SOLVED PROBLEM 7.10
A hoist powered by a 10-kW motor is used to raise a bucket filled with concrete and having a total mass
of 500 kg to a height of 80 m. If the efficiency of the hoist is 80 percent, find the time needed.

The upward force required is equal to the bucket’s weight mg. The power available is

P out = (Eff)P in = (0.8)(10 kW) = 8kW = 8000 W

Since P = W/t = Fs/t, here

2
Fs mgh (500 kg)(9.8 m/s )(80 m)
t = = = = 49 s
P P 8000 W
SOLVED PROBLEM 7.11
A horse has a power output of 1 kW when it pulls a wagon with a force of 400 N. What is the wagon’s
velocity?

Since P = Fv,

P 1000 W
v = = = 2.5 m/s
F 400 N
SOLVED PROBLEM 7.12
A motorboat requires 60 kW to move at the constant velocity of 4.5 m/s. How much resistive force does
the water exert on the boat at this velocity?
Since P = Fv,

4
P 6 × 10 W
4
F = = = 1.33 × 10 N = 13.3kN
v 4.5 m/s
SOLVED PROBLEM 7.13
◦
A 2400-lb car ascends a 10 slope at 30 mi/h. If the overall efficiency is 70 percent, what is the power
output of the car’s engine?
From Fig. 7-2 the weight w of the car has a component F along the slope of magnitude

◦
F = w sin θ = (2400 lb)(sin 10 ) = 417 lb