Help with Force problem

Question

An empty box of mass 0.2 kg is dropped on a hard surface from a height of 1.5m. Upon striking the surface, the box comes to rest in 0.5s. Find the average force exerted on the box as it comes to rest?

 

Answer 1

This is an impulse problem.  Find the change in linear momentum, set it equal to the impulse, and then solve for the force.

 

I = Ft = m(v₂ - v₁)

 

v₂  = 0  [comes to full stop]

v₁ = initial downward speed when the box contacts the floor, which you can get from energy conservation

 

gh = v₁²/2 ⇒ v₁ = √(2gh)

 

Ft = m[0 - √(2gh)]

 

F = -m√(2gh) / t

 

m = 0.2 kg

h = 1.5 meters

t = 0.5 s

g = 9.8 m/s²

 

Plug in the numbers and get F in Newtons.  The negative sign means the force opposes the direction of motion.