Spring Speed Problem: Solve 4kg Block, 3500N/m Stiffness

[timmy8]

Homework Statement

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?

Homework Equations

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

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.

 

[PhanthomJay]

timmy8, welcome to PF!

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

 

[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?

 

[PhanthomJay]

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?

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).

 

[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.

 

[PhanthomJay]

so in the spring potential should Uf be equal to zero?

yes

and for the change in gravitational PE isn't the formula m*g*delta_h? I am so lost.

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).

 

[timmy8]

i thought g would be -9.81?

 

[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

 

[PhanthomJay]

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

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.