Can Kinematics and Energy Conservation Solve the Egg Drop Problem?

[claudiairiond]

Homework Statement

An egg is dropped from a third-floor window and lands on a foam-rubber pad without breaking. If a 56.0g egg falls 12.0m from rest and the 5.00cm thick foam pad stops it in 6.25ms, by how much is the pad compressed? Assume constant upward acceleration as the egg compresses the foam-rubber pad. (Hing: Assume that the potential energy that the egg gains while the pad is being compressed is negligible.)

Homework Equations

Vf²=Vi²+2a∆y
∆y=((vi+vf)/2)*t
F=ma
KE_i + PE_i= KE_f+PE_f+W

The Attempt at a Solution

Separated the problem into two parts: first part when the egg travels through the air until it reaches the pad, then, when the egg hits the pad and compresses it.
Part 1:
V_f= 15.3 m/s
Therefore the acceleration of the egg going into the pad would be
a= (0m/s-15.3m)/.00625s
a= -2400m/s²
THEN
∆y= ((15m/s-0m/s)/2)*.00625s
∆y=.046875m

The pad is compressed 4.79cm!
BUT, I never took into account that the egg is 56 g!
How can I approach this using energy?!

 

[collinsmark]

BUT, I never took into account that the egg is 56 g!

Given the way the problem was stated, you don't really need to.

How can I approach this using energy?!

You can use conservation of energy as an alternate way to find egg's velocity as it hits the pad. The way you approached the problem using kinematics also works. But you can use conservation of energy to check you work if you wanted to.

o What is the gravitational potential energy of 56.0g egg at a height of 12 m?
o What's the formula for an object's kinetic energy as function of velocity, v?
o Invoking conservation of energy, solve for v.

(That gets you the velocity of the egg at the moment it hits the pad. You can't use conservation of energy after the egg hits the pad though [some of the energy is lost to heat].)

(You might want to go back and check your significant digits in your original attempt. You might have made a precision mistake or two.)