Stored Spring Energy Calculation

[lemon]

Hi - Would someone check my method here please?
Thank you

Homework Statement

Two trolleys A and B, of mass 0.70kg and 0.80kg respectively, are on a horizontal track and held together by a compressed spring. When the spring is released the trolleys separate freely and A moves to the left with an initial velocity of 4.0m/s.
Calculate:
a) the initial velocity of A
b) the energy initially stored in the spring

Homework Equations

F=ma

The Attempt at a Solution

a) (0.70x4.0)=(0.80xV)
v=(0.70x4.0)/(0.80)
v=3.5m/s

b) This is a transfer of elastic potential energy to kinetic energy -
Energy=1/2mv^2
mv=p(momentum)
1/2(0.70x4.0)^2 + 1/2(0.80x3.5)^2
=0.0392 + 3.92
=3.9592 J

 

[Doc Al]

a) (0.70x4.0)=(0.80xV)
v=(0.70x4.0)/(0.80)
v=3.5m/s

This is good. You used conservation of momentum.

b) This is a transfer of elastic potential energy to kinetic energy -
Energy=1/2mv^2
mv=p(momentum)
1/2(0.70x4.0)^2 + 1/2(0.80x3.5)^2
=0.0392 + 3.92
=3.9592 J

Your mistake here was squaring mv, instead of just v.
KE = 1/2mv^2, but you calculated 1/2(mv)^2. Not the same!

 

[lemon]

ahh of course:
silly boy!

(1/2x0.7x4.0^2) + (1/2x0.8x3.5^2) = 10.5 J

 

[Doc Al]

Now you've got it.

 

[lemon]

Thanks Doc