What Is the Common Velocity After Collision on a Frictionless Incline?

[mrshappy0]

Homework Statement

A block is on a frictionless incline. A block at the bottom of the incline is resting up the incline against a spring. The first block is released. The blocks stick and compress the spring. What is the common velocity immediately after collision?

Homework Equations

Kinetic energy of the two blocks + potential energy of blocks = potential energy of spring

The Attempt at a Solution

I am not concerned with solving this equation for the velocity. I am just concerned with understanding how to get to this equation. My exam useful equations study sheet shows that kinetic initial+ potential initial = kinetic final + potential final.

 

[mrshappy0]

Is the kinetic final canceled out because velocity would be zero at the final state?

 

[Doc Al]

I am just concerned with understanding how to get to this equation. My exam useful equations study sheet shows that kinetic initial+ potential initial = kinetic final + potential final.

That equation applies when mechanical energy is conserved. (Which is not the case during the collision of the two blocks.)

Is the kinetic final canceled out because velocity would be zero at the final state?

In the final position, the blocks are at rest. So their kinetic energy is zero.