Fundamental Engineering Concepts - Mathematics and Statistics for the Environment - page 232

Force B

Force A

(A)

Resultant

Force A

Force B

(B)

FIGURE 11.1 Force vector quantities.

force required to give 1 slug of mass an acceleration of 1 foot per second per second (ft/s 2 ). The new-
ton is defined as the force required to give 1 kilogram of mass acceleration of 1 meter per second
per second. A slug is the mass of 32.2 standard pounds. Since the mass of an object is commonly
expressed as its weight in pounds, we can make the conversion to slugs by dividing this weight by
the gravitational constant, g c = 32.2 ft/s 2 , for use in the following formula:

F = m × a × SF (11.2)

■ EXAMPLE 11.1
Problem: How much force must a seat belt be capable of withstanding to safely restrain a 180-
lb woman when her car comes to a sudden (i.e., 1-second) stop if initially traveling at 60 mph?
(Assume a safety factor of 4).

Solution:

m = (180 lb)/(32.3 ft/s 2 ) = 5.59 slugs

a = V / T = [(60 mph)(5280 ft/1 m)(1 hr/3600 s)]/1 sec = 88 ft/s 2

F = m × a × SF = 5.59 × 88 ft/s 2 × 4 = 1968 lb

Another important relationship where force is a key player is the concept of work . Work is the
product of the force and the effective displacement of its application point. The equation for calcu-
lating force is

W = F × s (11.3)

where
W = Work in foot-pounds (ft-lb).
F = Force in pounds (lb).
s = Distance in feet (ft).