Bending Stress on a Protective Cover

[Jesse Niekamp]

Homework Statement

A 30kg pallet falls from a height of 2m onto a protective cover. The cover has an area of 269m² and an overall thickness of 10.9mm.

a. What is the force/pressure on the cover?

b. What is the bending stress on the cover?

Homework Equations

F=ma
bending stress = mc/I
P=F/A
Vf^2=Vi^2+2ad
KE=mgh
Wnet=1/2m(Vf)^2-1/2m(Vi)^2

The Attempt at a Solution

F=ma=(30)(9.81)=294.3N
P=F/A=294.3/269=1.094Pa
Vf^2=0+2(9.81)(2)...Vf=6.264m/s
KE=mgh=(30)(9.81)(2)=588J

 

[haruspex]

F=ma=(30)(9.81)=294.3N
P=F/A=294.3/269=1.094Pa

That F will be the steady state force. It does not take into account the impact from the fall.
During impact, force will be a function of time, increasing up to some max then dropping back down (the mass might even bounce). The peak force will depend on the flexibility of the cover, which we are not given. The more flexible, the longer the duration of the impact and the less the peak force. It will be a damped oscillator.

As for the pressure, I see no suggestion that the mass spreads right across the cover. The localised pressure could be much higher.

Where does this very flawed question come from?