An 3.7 lb hammer head, traveling at 5.8 ft/s strikes a nail and is brought to a stop in 0.00068 s. The acceleration of gravity is 32 ft/s 2. What force did the nail receive? Answer in units of lb.

31677.2 lb

Explanation:

mass of hammer (m) = 3.7 lb

initial velocity (u) = 5.8 ft/s

final velocity (v) = 0

time (t) = 0.00068 s

acceleration due to gravity (g) 32 ft/s^{2}

force = m x (a + g)

where

m is the mass = 3.7 lb g is the acceleration due to gravity = 32 ft/s^{2} a is the acceleration of the hammer

from v = u + at

a = (v-u) / t

a = (0-5.8) / 0.00068 = - 8529.4 (the negative sign showa the its decelerating)

we can substitute all required values into force = m x (a+g)

force = 3.7 x (8529.4 + 32) = 31677.2 lb