Consider a frictionless track as shown in Figure. A block of mass m1 = 5.00 kg is released from A . It makes a head-on elastic collision at B with a block of mass m2 = 10.0 kg that is initially at rest. Calculate the maximum height to which m1 rises after the collision.

Energy and collisions. Is the theme of this problem today. Why energy?. Using theorem conservation of mechanical energy we will find the initial velocity of m1 before the collision. Then using the theory of elastic collisions we will get the final velocity of m1 after the collision. Finally we will use the theorem of conservation of mechanical energy to find the desired height.
We go with the first part of the problem. Find the initial velocity before the collision will have the mass m1. To do this we make the energy balance between points A and B.
We must emphasize that right now all this energy on the point A is only potential energy. When m1 reach the point B. all its potential energy it will be converted into kinetic energy.

In an elastic collision two quantities remains the momentum and kinetic energy. The conservation of momentum equation is expressed in the equation (1). for the conservation of kinetic energy we will use its linear form expressed in equation (2). From there we will find the final velocity of m1 after the collision.

Now, we just do the energy balance between B and D. The change is that now the kinetic energy present at point B becomes potential energy at point D at a certain height h2. That we will obtain from the energy balance described above:

With this we have solved the problem in its entirety. Such problems are easy to solve. as long as we are organized. we just ask. what we want?. What do we need to get it ?. How to get what we need ?. in our case was:
What we want? final height after collision
What do we need to get it ? the final velocity after collision
How to get what we need? using an energy balance that allowed us to obtain the value of the initial velocity before the collision.
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