Question

The acceleration of gravity is 9.81 m/s 2 . If a 56.4 g egg falls 14.0 m from rest and the 7.85 cm thick foam pad stops it in 6.05 ms, by how much is the pad compressed? Assume constant upward acceleration as the egg compresses the foam-rubber pad.

Answer 1

The pad is compressed by 5.02 cm

Step-by-step explanation:

First of all, we have to calculate the initial mechanical energy of the egg, which is equal to its gravitational potential energy at the top:

`E=GPE=mgh`

where

`m=56.4 g = 0.0564 kg` is the mass of the egg

`g=9.8 m/s^2` is the acceleration due to gravity

h = 14.0 m is the initial height

Substituting

`E=(0.0564)(9.8)(14.0)=7.74 J`

As the egg falls down, this energy is conserved and it is entirely converted into kinetic energy; so, when the egg reaches the pad, its energy is now equal to its kinetic energy:

`E=(1)/(2)mu^2`

where

u is the velocity of the egg as it reaches the pad

Solving for u,

`u=\sqrt{(2E)/(m)}=\sqrt{(2(7.74))/(0.0564)}=16.6 m/s`

Then, the egg is stopped by the pad, so it has a uniformly accelerated motion; so we can find the distance it takes to stop by using the suvat equation

`s=((u+v)/(2))t`

where:

u = 16.6 m /s is the initial velocity

v = 0 is the final velocity

`t=6.05 ms = 6.05\cdot 10^(-3)s` is the stopping time

Solving,

`s=((16.6+0)/(2))(6.05\cdot 10^(-3))=0.0502 m = 5.02 cm`

So, the pad is compressed by 5.02 cm.