# Conservation of Energy Problem with spring

1. Apr 21, 2012

### JacksonL

1. The problem statement, all variables and given/known data
A vertical Spring (ignoring mass) whose spring constant is 875N/m is attached to a table and is compressed down by .160m. What upward speed can it give to a .350kg ball when released? How high up its original position will the ball fly?

2. Relevant equations
Spring constant = 1/2Kx^2
Potential energy with gravity = mgh

I'm guessing my equation would look something like this?

1/2mv1+mgy1=1/2mv2+1/2kx2

3. The attempt at a solution

I'm not sure if I'm doing this right so far. This is all I've gotten to.

2. Apr 22, 2012

### JacksonL

any assistance?

3. Apr 22, 2012

### darkxponent

Ok tell me if you have studied these things.
1) Kinetic Energy
2) Potential Energy
2) Work Energy Theorem

4. Apr 22, 2012

### JacksonL

Yes I've learned about each of those.

5. Apr 22, 2012

### darkxponent

I asked it because the formulas written are not correct.

6. Apr 23, 2012

### JacksonL

The work energy theorem is:

1/2mv^2-1/2mv^2.

Translational kinetic energy is 1/2mv^2

7. Apr 23, 2012

### Curious3141

That doesn't make any sense. The work energy theorem is an equation, and should have a left hand side and an equal sign. And 1/2mv^2-1/2mv^2 = 0. Please put the relevant subscripts.

At any rate, you don't need that form of the work-energy theorem here.

You do need this, though:

And this is written correctly. You don't need $v_1$ and $v_2$ here, because the ball starts at rest. Just use one variable for the speed at which the ball is launched, $v$.

When solving this, consider the spring and ball as a single system. You compress the spring with the ball on top of it, release it, the spring stretches to its original length carrying the ball with it, following which the ball continues to move vertically upward (it's "launched"). Now ask yourself the following:

1) When the spring is fully compressed, what form of energy resides in the system? How do you calculate this?

2) As the spring is released and is relaxing to its original length, what energy transformations are taking place? What energy is decreasing? What's (or what are) increasing?

3) Finally, when the spring attains its original length, what forms of energy exist in the system?

Equate the energy in state 1 to that in state 3 with Conservation of Energy. Now write down the relevant equations. You can now solve for the initial kinetic energy and thereby, the initial upward speed of the ball at the point of launch.

Continuing on, the ball travels upward until it reaches a maximum height, when it becomes momentarily stationary.

4) What form of energy exists in the ball at this time? Again use conservation of energy to solve for the maximum height the ball attains. Remember that this height is taken from the point of launching. The question is asking for how high the ball gets from its *original* position. What do you need to do?

Last edited: Apr 23, 2012