Calculate Friction in Spring hanging from ceiling

[cellurl2]

Homework Statement

A massless spring with force constant k = 200N/m hangs from the ceiling. A 2.0 kg weight is attached to the free end of the spring and released. If the weight falls 17 cm before starting back upwards, how much work is done by friction during its decent? (Note: choose ground zero for gravitational potential energy to make this easy!)

Homework Equations

Hooks Law;
E=1/2*k*x*x

The Attempt at a Solution

http://www.wikispeedia.org/tmp/untitled.png
E= 1/2 * 200 * 0.098 * 0.098 Joules

What is worries us is that we didnt use the 17cm in our solution.

Thanks

 

[gneill]

Hi cellurl2, Welcome to Physics Forums.

Start by identifying all the places that energy can be stored, come from, or go, in the system.

 

[cellurl2]

(corrected)
PE lost is m*g*deltah = 2kg*9.8*0.17m= 3.332 joules

PE gained by spring= 1/2 * k * x* x = 1/2 * 200N/m * 0.17m*0.17m= 2.89 joules

So? is that it , friction (spring tension/heat??) just 3.332-2.89= 0.442 joules

 

[gneill]

PE lost is m*g*deltah = 2kg*9.8*0.17m= 3.332 joules

PE gained by spring= 1/2 * k * x* x = 1/2 * 100N/m * 0.17m*0.17m= 1.445 joules

Check the value that you used for the spring constant.

So? is friction loss (whatever that is? spring heat) just the difference??

As it turns out, yes, it will be the difference. Energy is lost from the system due to frictional heating.

This is why I suggested that you start by identifying all the places that energy can reside or got to in the system. Once you've done that, these sorts of problems become a matter of summing things up accordingly for the given scenarios.

It's important to understand the assumption you've made: You have assumed (correctly) that there will not be any kinetic energy involved at the two positions that you've chosen to compare the energy in the system. In other problems of this type you may be given information about the instantaneous velocity at some position that is not at an extreme of the motion.