# Conservation of energy

1. Mar 22, 2016

### Janiceleong26

1. The problem statement, all variables and given/known data

I'm working on the second part of this question and I want to find the initial speed before P strikes the barrier.
So I used principle of conservation of energy,
K.E at Equilibrium position + elastic p.e. at Equilibrium positon = K.E just before it strikes the barrier + G.P.E at the barrier

But according to the solutions,

Why Is the e.p.e when extension is (a+l/20) included? I thought the string is cut, so there shouldn't be any tension anymore

2. Relevant equations

3. The attempt at a solution

2. Mar 22, 2016

### PeroK

If the mass is hanging on the string, then there will be tension in the equilibrium position. The tension in the string must balance the gravitational force on the mass.

3. Mar 22, 2016

### haruspex

The KE when descending through the equilibrium position will be the same as when ascending through it.
It starts with no KE, but elastic PE corresponding to an extension of a+l/20, a being the equilibrium extension. In rising to the equilibrium position, it gains mgl/20 in GPE, but its extension decreases to a. Thus the gain in KE is EPE(a+l/20)-EPE(a)-GPE(l/20).

4. Mar 22, 2016

### Janiceleong26

Ok thank you.