FInd force given weight, time, velocity and gravity

Question

A(n) 4.4 lb hammer head, traveling at 6 ft/s strikes a nail and is brought to a stop in 0.00084 s. The acceleration of gravity is 32 ft/s 2 . What force did the nail receive? Answer in units of lb.

Answer 1

The Impulse-Momentum Theorem states that the Impulse equals the change in momentum

The impulse is calculated as force multiplied by time (F•t)

Momentum is calculated as mass multiplied by velocity (m•v) so the change in momentum for a single object of mass "m" is m(v₂ - v₁) where v₂ is the final velocity (velocity at time 2) and v₁ is the initial velocity (velocity at time 1)

So: F•t = m(v₂ - v₁)

Plug in the numbers and solve.

The issue with this problem is the units. You are told that the hammer head is 4.4 lb. That typically means lbs force or weight in pounds and by Newton's second law m = wg so you would probably use this to calculate the mass that goes into the impulse-momentum equation. BUT, it's possible you are being given a mass of 4.4 lb mass. I doubt it, but I have no idea how your book works. Anyway, MAKE SURE TO CHECK THE UNITS!!

Answer 2

F = m(v - 0)/Δt = 4.4lb/32ft/s²·6ft/s/0.00084s = 982.143 lb