Energy Problem involving Spring

[testme]

Homework Statement

A block of mass 1.0 kg, at rest on a horizontale table, is attached to two rigid supports by springs A and B. A force of 10.0 N strecthes spring A alone by 0.25 m while a force of 2.5 N extends spring B alone by the same amount. Initially the block is at rest between unstretched springs; then it is pushed to the side a distance of 0.50 m, compressing one spring and extending another.

a) What is the total work done to move the block. (The block is held at rest.)
b) If the block is released with what velocity does it move through its original equilibrium position?
c) What would be the spring constant of a single spring that would duplicate A and B?

mass of block = 1.0 kg
Force to stretch spring A by 0.25 m = 10.0 N
Force to stretch spring B by 0.25 m = 2.5 N
side distance pushed = .5 m

Homework Equations

W = FΔd
Ee = 1/2kx^2
Ek = 1/2mv^2

The Attempt at a Solution

a) W = Fd
= (10 + 2.5)(0.5)
= 6.25 J

b) Not sure how to do this I think it has something to do with the energy but not sure exactly what it's asking for. From what I understood it'd be something like

1/2(k1)x^2 + 1/2(k2)x^2 + 1/2mv^2 = 1/2(k1)x^2 + 1/2(k2)x^2

 

[gneill]

a) W = Fd
= (10 + 2.5)(0.5)
= 6.25 J

The force produced by a spring does not remain constant with distance. So you'll either have to integrate F*dx or use the 'canned' expression for spring potential energy.

It happens to be a fluke of the numbers for this problem that your 'method' above gives the same result as the correct methods.

b) Not sure how to do this I think it has something to do with the energy but not sure exactly what it's asking for. From what I understood it'd be something like

1/2(k1)x^2 + 1/2(k2)x^2 + 1/2mv^2 = 1/2(k1)x^2 + 1/2(k2)x^2

Something like that

What's the total energy that system holds? Give it a name (say, E).

When the block is at the equilibrium position, how much potential energy is in the springs? Where must the rest be?