Page 70 - Schaum's Outline of Theory and Problems of Applied Physics

CHAP. 5] LAWS OF MOTION 55

and its acceleration is
v 44 ft/s
a = = = 5.5 ft/s 2
t 8s
Hence

2
F = ma = (100 slugs)(5.5 ft/s ) = 550 lb

FREE-BODY DIAGRAMS AND TENSION
In all but the simplest problems that involve the second law of motion, it is helpful to draw a free-body diagram
of the situation. This is a vector diagram that shows all the forces which act on the body whose motion is being
studied. Forces that the body exerts on anything else should not be included, since such forces do not affect the
body’s motion.
Forces are often transmitted by cables, a general term that includes strings, ropes, and chains. Cables can
change the direction of a force with the help of a pulley while leaving the magnitude of the force unchanged. The
tension T in a cable is the magnitude of the force that any part of the cable exerts on the adjoining part (Fig. 5-1).
The tension is the same in both directions in the cable and T is the same along the entire cable if the cable’s mass
is small. Only cables of negligible mass will be considered here, so T can be thought of as the magnitude of the
force that either end of a cable exerts on whatever it is attached to.

Fig. 5-1

SOLVED PROBLEM 5.17

A 1200-kg elevator is supported by a cable in which the maximum safe tension is 14,000 N. (a) What is
the greatest upward acceleration of the elevator? (b) The greatest downward acceleration?

(a) The elevator’s weight is
2
w = mg = (1200 kg)(9.8 m/s ) = 11,760 N