# Maximum distance an object travels when released by a spring force.

1. Mar 29, 2013

### Yankeedogg

1. A block of mass 0.247 kg is placed on top of a light, vertical spring of force constant 5 050 N/m and pushed downward so that the spring is compressed by 0.109 m. After the block is released from rest, it travels upward and then leaves the spring. To what maximum height above the point of release does it rise? (Round your answer to two decimal places.)

2. Not sure how to set up an equation to solve for the distance.

3. The attempt at a solution

2. Mar 30, 2013

### Simon Bridge

Welcome to PF;
That's a problem that gives many students pause.
... hint: conservation of energy.

3. Mar 30, 2013

### rude man

Is that 0.109m compressed from the relaxed position before the weight is placed, or is it after the weight is placed? Need to find out, especially since the answer calls for 2 decimal-place accuracy.
.

4. Mar 30, 2013

### Yankeedogg

Rude Man, the question is posted exactly how i received it.

5. Mar 30, 2013

### Yankeedogg

I got it. Yc=kx^2/2mg+Ya where k=5050N/m, x=.109, m=0.247kg, g=9.8m/s^2 and Ya= 0m because Ya is where the spring returns to its resting position and Yb is where the spring is compressed to 0.109m. Therefore, the maximum height above the spring the object reaches is 12.39m.

Equation was taken from k= 2mg (Yc-Ya)/x^2

6. Mar 30, 2013

### Simon Bridge

How did you come to choose that equation?
(i.e. did you understand the problem?)

7. Mar 30, 2013

### Yankeedogg

From a similar problem on an example in my textbook.

8. Mar 30, 2013

### rude man

Then you should ask. I admit it doesn't make too much difference since the spring is so strong and the mass so light - but to 2 decimal points I think it might well.

Mr Bridge, what are you assuming?

9. Mar 30, 2013

### Simon Bridge

@Yankeedog: so that's a "no" then? You do not understand why the similar problem was solved using that relation? Then how do you know it's the right one?

Did you try applying conservation of energy to help you understand the problem?
Do you see what difference rude man's observation makes to the answer?

@rude man: I try not to assume - unless donkeys are involved.

10. Mar 30, 2013

### rude man

11. Mar 31, 2013

### Simon Bridge

OP did - post #5 ;)