Page 165 - Schaum's Outline of Theory and Problems of Applied Physics

150 SIMPLE MACHINES [CHAP. 12

Since the plank is 3 m long (Fig. 12-6),
L in + L out = 3m

L in = 3m − L out
In the absence of friction,
F out L in
=
F in L out
980 N 3m − L out
=
350 N L out
3.8L out = 3m
L out = 0.79 m
The fulcrum should be located 79 cm from the end of the crate.

F out
L
in
F in L out
200 kg

Fig. 12-6

SOLVED PROBLEM 12.8

The wheel and axle (Fig. 12-7) is a development of the lever that permits continuous motion. (a) Where
is the fulcrum? (b) What is the IMA of a wheel and axle?

Fig. 12-7

(a) The center of the axle acts as the fulcrum.
(b) The input force acts tangentially on the wheel rim, and the output force acts tangentially on the axle rim. When
the combination makes one complete turn, a point on the wheel moves through s in = 2π R and a point on the
axle moves through s out = 2πr. Hence
2π R R
s in
IMA = = =
s out 2πr r
The larger the wheel radius relative to that of the axle, the greater the mechanical advantage.