Final velocity of two blocks between a spring

AI Thread Summary
The discussion centers on calculating the final velocities of two blocks released from a compressed spring. Block A has a mass of 1 kg and Block B has a mass of 3 kg, with a spring constant of 720 N/m and initial compression of 0.225 m. The user correctly calculated the accelerations as 162 m/s² for Block A and 54 m/s² for Block B but struggled with determining the final speeds. Initial attempts using conservation of energy yielded incorrect results, while the expected final speeds are 5.23 m/s for Block A and 1.74 m/s for Block B. The conversation emphasizes the need for applying conservation laws to solve for the final velocities accurately.
PedroPicapiedra
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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
 
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PedroPicapiedra said:

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.
 
... and you will need to use another conservation law.
 

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