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302 MECHANICS.
Solution
:
x = (5
2 — (4^)
2
) X 520
x — (25 — 20X) X 520
x = \% X 520 = 2470 foot-pounds of energy given
out by the fly-wheel during this change of speed.
Example 3.
How much stored energy is left in the wheel after its angu-
lar velocity is reduced to 4>i feet per second ?
Solution
:
K = (±/
2 )
2
X 520 = 20X X 520 = 10,530 foot-pounds.
The same result may be obtained by subtracting, thus :
13,000 — 2470 =10,530 foot-pounds.
Centrifugal Force.
The centrifugal force is the force with which a revolving
body tends to depart from its center of motion and fly in a
direction tangent to the path which it describes. The centrip-
etal force is the force by which a revolving body is prevented
from departing from the center of motion. When the centri-
fugal force exceeds the centripetal force the body will move
away from the center of motion, but if the centripetal force ex-
ceeds the centrifugal force, the body will move toward the center
of motion. The centrifugal force in any revolving body is equal
to the mass of the body (see page 286) multiplied by the square
of its velocity, and this product divided by the radius of the
revolving body.
, WXv2
m X v2
32.2 X r~ r
cf= Centrifugal force in pounds.
r = Radius in feet.
i) — Velocity in feet per second.
W= Weight of moving body in pounds.
m = Mass of moving body.
Example.
The weight a, in Fig. 11, is four pounds, and the length of
the string is two feet; the weight is made to swing around the
center c, three revolutions per second. What is the stress on
the string due to centrifugal force ?
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