Solve Spring Compression Problem: Work & Energy Approach

[reklaws89]

Homework Statement

Use work and energy to solve the following. A .1 kg ball is placed against a massless spring that has a stretch constant 50,000 N/m and is compressed 2 m. The spring fires the ball straight up. a) How far did the ball rise assuming no friction? b) The ball's actual rise was 2m short of the answer in part A. What was the frictional work done by air?

Homework Equations

1/2ky^2=mg(h+y)

The Attempt at a Solution

I figured out part A to be 102,038 m... which seems outrageous, but the numbers in this problem are also outrageous. I'm really just struggling on how to do B or even attempt it.

 

[G01]

You need to show some work to get help here. How did you end up with your answer in part a?

 

[reklaws89]

I used the equation (KE + PEg + PEs)i = (KE + PEg + PEs)f

KEi=0
KEf=0
PEgi=0
PEsf=0

PEsi=1/2ky^2
(y=compression)
PEgf=mg(h+y)
(h=distance traveled)

therefore, 1/2ky^2=mg(h+y)
so 1/2(50,000N/m)(4m)^2=.1kg(9.8m/s^2)(h+2m)
100,000Nm=.98N(h+2m)
102,040m=h+2m
102,038m=h

 

[PhanthomJay]

Looks correct, but as you say, the numbers given are outrageous. And if air friction causes the ball to stop 2 feet short of 102,038', that's not even significant enough to bother with. I think the problem just chose a poor set of numbers. But for part B, in general, what do you know about the relationship between work done by non conservative forces, and mechanical energy?