Question

A hammer of mass m falls from rest off of a roof and drops a height H onto your head.

a) Assuming that the tool is in actual contact with your head for a time △t before it stops and slides off, what is the algebraic expression for the average force it exerts on your skull while stopping?

Answer 1

For conservation of energy we have to:
mgH=mv²/2
Clearing
v=sqrt(2gH)
Then, by definition
F=Δp/Δt= Δ(mv)/ Δt=m Δ(v)/Δt=
=m[sqrt(2gH)-0]/Δt= m[sqrt(2gH)]/ Δt
the answer is
F=m[sqrt(2gH)]/ Δt