(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A spring of negligible mass and force constant k=400 is hung vertically and a 0.2kg pan is suspended from its lower end. A butcher drops a 2.2kg steak onto the pan from a height of 0.4m. The steak makes a totally inelastic collision with the pan and sets the system into vertical SHM. What is the speed of the pan and steak immediately after the collision?

2. Relevant equations

PE=mgh

KE=mv^2/2

mv=mv

E(total energy in spring)=kA^2/2

3. The attempt at a solution

First I found out the energy produced from dropping the steak 0.4m:

PE=mgh

=2.2kg(9.8)(0.4m)

=8.624J

Then I used this to find the speed of the steak before the collision:

PE=KE

8.624J=(2.2kg)(v^2)/2

v=2.8m/s

When the steak goes into the pan by conservation of momentum we have:

mv=mv

(2.2kg)(2.8m/s)=(2.4kg)(v)

v=2.56666666m/s

My problem:However if I plug 2.566666m/s back into the KE equation I do not get 8.624J, instead I get 7.095J which means that the energy is not conserved? Do you guys know why? If I have 7.095J as the energy and I plug it into the E(total energy in spring) equation I do not get the right amplitude, instead plugging in 8.624J will get me the right answer.

HERE IS A SIMPLER PROBLEM

I found the same problem when solving for the final velocity of a block m=0.992kg when a bullet with v=280m/s and m=0.008kg strikes it and embeds itself into it.

By conservation of momentum:

(0.008)(280)=(1kg)(v)

v=2.24m/s

Where initially the KE in the bullet initially is

KE=0.008(280)^2/2=313.6J

But the KE after the collission is

KE=1kg(2.25m/s)^2/2=2.5088J

So clearly the energy is not conserved??? I am confused.

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Conservation of momentum/mass when dropping an object on a spring.

**Physics Forums | Science Articles, Homework Help, Discussion**