a 1.00 kg block compresses a spring for which K1 = 100 N/m by 20.0 cm and is then released to move across a horizontal, frictionless table, where it hits and compresses another spring for which K2 = 50 N/m. Determine:

a) the total mechanical energy of the system
b) the speed of the mass while moving freely between springs, and
c) the maximum compression of the second spring

Question

a 1.00 kg block compresses a spring for which K1 = 100 N/m by 20.0 cm and is then released to move across a horizontal, frictionless table, where it hits and compresses another spring for which K2 = 50 N/m.  Determine:

a) the total mechanical energy of the system
b) the speed of the mass while moving freely between springs, and
c) the maximum compression of the second spring

alfie · Answer

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Alright this is the situation. 
In the initial situation we have the following...

$$P_e = \frac{1}{2}kx^2$$

And that's pretty much it, let's we see in the moment when the spring lets go the block.
All the Potential energy of the spring is transformed to kinetic energy.

$$\frac{1}{2}kx^2 = \frac{1}{2}mv^2$$

This way you can solve for v and get the velocity.