# Spring potential energy and mass

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1. Oct 29, 2015

### kolua

1. The problem statement, all variables and given/known data
One end of a vertical spring of spring constant k = 1900 N/m is attached to the floor. You compress the spring so that it is 2.50 m shorter than its relaxed length, place a 1.00-kg ball on top of the free end, and then release the system att = 0. (All values are measured in the Earth reference frame.)

A. By how much does the mass of the spring change during the time interval from t = 0 to the instant the ball leaves the spring?

B. By how much does the mass of the Earth-ball-spring system change during the time interval from t = 0to the instant the ball reaches its maximum height?

2. Relevant equations
ΔE=Δmc2
Us=1/2 kx2

3. The attempt at a solution
ΔE=ΔU=1900/2×2.52=5937.5
Δm=5937.5/9/188=6.597×10-6
is this correct for question A?
I'm not sure if the mass changes because the instant the ball leaves the potential energy is converted to the ball's kinetic energy. And there should be no change in mass?

For question B, how should I approach?

2. Oct 29, 2015

### haruspex

That looks right for a).
For b), what energy has entered or left the Earth-spring-mass system?

Last edited: Oct 29, 2015
3. Oct 29, 2015

### Mister T

Well, it's not an instantaneous process. As the spring relaxes the ball picks up speed, so the process takes as long as it takes for the spring to go from it's compressed state to its relaxed state. And during the process the ball rises, so there's also an increase in the gravitational potential energy of the ball-Earth system.

Change in mass of the spring, or change in mass of the whole system?

4. Oct 30, 2015

### kolua

potential energy and kinetic energy?

5. Oct 30, 2015

### haruspex

Those are both internal to the Earth-spring-mass system.

6. Oct 30, 2015

### kolua

So should I count the mass of the ball and the earth intot the calculation for this one?

7. Oct 30, 2015

### Mister T

What haruspex is trying to get you to do is determine which of these energies is leaving or exiting the system. Note that the choice of system is arbitrary. It's different in Parts A and B of this problem.

8. Oct 31, 2015

### kolua

For question A, since there is only the spring in the system, there is only the change in the spring potential energy, which is U=1/2 kx2 = E=mc2, is this correct?
For question B, there are potential and kinetic energy for this system, so U=1/2 kx2=E-K? is this right?

9. Oct 31, 2015

### Mister T

Best to think of it in terms of states of the system. The initial state has energy $E_i$ and the final state has energy $E_f$. In this way you can account for kinetic energy and both types of potential energy. Something you're not doing now is including both types of potential energy.

10. Oct 31, 2015

### kolua

Uspring=1/2 kx2=E-K-Ugravity?

11. Oct 31, 2015

### Mister T

Ok, but you're not solving for $U_{spring}$.

12. Oct 31, 2015

### kolua

Δmc2=K+Ugravity?

13. Oct 31, 2015

### Mister T

I think you should explain briefly what you're doing to get these expressions. In particular, go back and read the statement of the problem, then read Post #9 and follow the scheme outlined there.
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