Spring Speed Problem

1. Nov 9, 2009

timmy8

1. The problem statement, all variables and given/known data
A spring whose stiffness is 3500 N/m is used to launch a 4 kg block straight up in the classroom. The spring is initially
compressed 0.2 m, and the block is initially at rest when it is released. When the block is 1.3 m above its starting
position, what is its speed?

2. Relevant equations
System: block, spring and earth.
delta_Uspring + delta_Ugravitation + delta_K=0

3. The attempt at a solution
everything i've tried seems to be wrong, the answer answer given to us however is 3.09 m/s.

2. Nov 9, 2009

PhanthomJay

timmy8, welcome to PF!

Your equation is correct, so please show your work so we may see where you may have gone wrong.

3. Nov 9, 2009

timmy8

1/2(3500)(1.3^2)-1/2(3500)(0.2^2)+4(-9.8)(1.3-0.2)+1/2(4)Vf^2-1/2(4)(0^2)=0

from there i solved for vf^2;

and vf^2=-1422.19

i am getting Vf^2 to be a negative number and i would have to solve the square root of that to get Vf.
what am i doing wrong?

4. Nov 9, 2009

PhanthomJay

You have the change in the spring potential energy wrong. What is the PE of the spring when the block rises 1.3 m above its start point? The block is not attached to the spring. Also, you seem to have slipped up on a plus /minus sign for the change in gravitational PE. Also, the problem asks for the speed at 1.3 m above the initial start position of the block (when the spring is initially compressed, I think).

5. Nov 9, 2009

timmy8

so in the spring potential should Uf be equal to zero? and for the change in gravitational PE isn't the formula m*g*delta_h? I am so lost.

6. Nov 9, 2009

PhanthomJay

yes
Yes, the formula is change in Gravitational PE is (mgh_final) - (mgh_initial). final h is 1.3 and initial h is zero, so the change is positive (it has gained grav. PE).

7. Nov 9, 2009

timmy8

i thought g would be -9.81?

8. Nov 9, 2009

timmy8

now i have:
-springPE +mgh_final+1/2(m)v_final^2=0

This gave me the correct answer.

thank you for all your help PhantomJay

9. Nov 10, 2009

PhanthomJay

You're welcome. The plus and minus sign can be a killer in Physics, and it is easy to get confused. Sometimes you just have to reason it out.