# Final velocity of two blocks between a spring

## Homework Statement

Two blocks have a spring compressed between them, Block A (mass 1kg) and block B (mass 3kg) . The spring has force constant 720 N>m and is
initially compressed 0.225 m from its original length. For each
block, what is (a) the acceleration just after the blocks are released;
(b) the final speed after the blocks leave the spring?

## Homework Equations

Fspring = kx = ma
1/2kx^2 = 1/2 mv^2

## The Attempt at a Solution

For a I got
Aa = 162m/s^2
Ab = 54m/s^2

However I cannot for the life of me figure out b. I have tried using kinematic equations and conservation of energy.
1/2(720N)(0.225)^2 = 1/2(1kg)(v)^2
Gives me 6.03m/s for the 1kg mass
and 3.4m/s for the 3kg mass.
I know these results are wrong. They are supposed to be 5.23m/s and 1.74m/s
Thanks

ehild
Homework Helper

## Homework Statement

Two blocks have a spring compressed between them, Block A (mass 1kg) and block B (mass 3kg) . The spring has force constant 720 N>m and is
initially compressed 0.225 m from its original length. For each
block, what is (a) the acceleration just after the blocks are released;
(b) the final speed after the blocks leave the spring?

## Homework Equations

Fspring = kx = ma
1/2kx^2 = 1/2 mv^2

## The Attempt at a Solution

For a I got
Aa = 162m/s^2
Ab = 54m/s^2

However I cannot for the life of me figure out b. I have tried using kinematic equations and conservation of energy.
1/2(720N)(0.225)^2 = 1/2(1kg)(v)^2
Gives me 6.03m/s for the 1kg mass
and 3.4m/s for the 3kg mass.
I know these results are wrong. They are supposed to be 5.23m/s and 1.74m/s
Thanks
The initial potential energy of the springs converts to the kinetic energy of both masses, 1/2mAvA2+1/2mBvB2.

haruspex
Science Advisor
Homework Helper
Gold Member
2020 Award
... and you will need to use another conservation law.