Conservation of energy with spring

[fanie1031]

1. A spring of constant 22 N/m is compressed a distance 8 cm by a 0.4kg mass, then released. It skids over a frictional surface of length 2.3m with coefficient of friction 0.17, then compresses the second spring of constant 2N/cm. The acceleration of gravity is 9.8m/s(squared). How far will the second spring cmpress in order to bring the mass to a stop? Answer in cm.



2.

W=Fd
.5mgyf + .5Kdelta(X squared) = .5mgyo + .5Kdelta(Xsquared)
also mgyf + 1/2mVf^2 = mgyo + 1/2mVo^2



3. I used all three formulas but the fact that I'm using cefficients is throwing me off.

 

[alphysicist]

Hi fanie1031,

1. A spring of constant 22 N/m is compressed a distance 8 cm by a 0.4kg mass, then released. It skids over a frictional surface of length 2.3m with coefficient of friction 0.17, then compresses the second spring of constant 2N/cm. The acceleration of gravity is 9.8m/s(squared). How far will the second spring cmpress in order to bring the mass to a stop? Answer in cm.



2.

W=Fd

For consant forces the work done is:

$$W=F d \cos\theta$$
where theta is the angle between the force and the displacement of the object. What would theta be for the work done by this frictional force? What would F and d be?

.5mgyf + .5Kdelta(X squared) = .5mgyo + .5Kdelta(Xsquared)
also mgyf + 1/2mVf^2 = mgyo + 1/2mVo^2

These two formulas do not apply to this problem. A good starting point for these problems is:

$$W_{\rm nc} = E_f - E_i$$

which means

(work done by non-conservative forces during displacement) = (energy at end of displacement) - (energy at beginning of displacement)


What does this give?