How do I calculate elastic potential energy?

[alicia12131415]

Homework Statement

A 0.29-kg cart and a 0.19-kg cart are held together with a compressed spring between them. When they are released, the 0.29-kg cart moves at 1.1 m/s to the right.
How much elastic potential energy was stored in the spring before the release?

Relevant Equations

U = (1/2)kx^2
k = spring force constant
x = stretch length

Is this the correct formula to use, if not what is. I really just don't know where to start. I really just need to know where and how to start.

 

[collinsmark]

Hello @alicia12131415,

Welcome to PF!

Problem Statement
A 0.29-kg cart and a 0.19-kg cart are held together with a compressed spring between them. When they are released, the 0.29-kg cart moves at 1.1 m/s to the right.
How much elastic potential energy was stored in the spring before the release?
Relevant Equations
U = (1/2)kx^2
k = spring force constant
x = stretch length

Is this the correct formula to use, if not what is. I really just don't know where to start. I really just need to know where and how to start.

Try using conservation of energy.

What's the kinetic energy of the 0.29 kg kart? What's the kinetic energy of the 0.19 kg kart? (Hint: that last calculation is also going to involve conservation of momentum.)

I'm guessing that the problem wants you to treat the spring itself as ideal and massless.

 

[alicia12131415]

So, I got

Velocity for 0.19 kg cart:
0 = (0.29kg)(1.1m/s) + (0.19)v_2f
v_2f = −1.6789 m/s

Kinetic energy:
0.29 kg KE_1f = (1/2)(0.29kg)(1.1m/s)² = 0.17545 J
0.19 kg KE_2f = (1/2)(0.19kg)(-1.6789m/s)² = 0.26781 J
KE_f = 0.44326 J
ΔKE = 0.44326 J - 0 J = 0.44326 J

Conservation of Energy:
KE_i + PE_i = KE_f + PE_f
PE_i = ΔKE + PE_f
PE_i = 0.44326 J + 0 J = 0.44326 J

Is this correct?

 

[haruspex]

So, I got

Velocity for 0.19 kg cart:
0 = (0.29kg)(1.1m/s) + (0.19)v_2f
v_2f = −1.6789 m/s

Kinetic energy:
0.29 kg KE_1f = (1/2)(0.29kg)(1.1m/s)² = 0.17545 J
0.19 kg KE_2f = (1/2)(0.19kg)(-1.6789m/s)² = 0.26781 J
KE_f = 0.44326 J
ΔKE = 0.44326 J - 0 J = 0.44326 J

Conservation of Energy:
KE_i + PE_i = KE_f + PE_f
PE_i = ΔKE + PE_f
PE_i = 0.44326 J + 0 J = 0.44326 J

Is this correct?

Looks good, but you should round the answer to match the fewest significant digits of the given data.

 

[alicia12131415]

I will, thank you for checking my work. Have a wonderful weekend.