How Fast Must a Block Slide to Circle a Loop After Inelastic Collision?

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To determine the minimum speed required for a block to circle a loop after an inelastic collision, the problem begins with a block of mass m sliding on a frictionless track and colliding with a stationary block of mass M. The conservation of energy principle is applied, where the initial potential and kinetic energy must equal the final potential and kinetic energy. The key is to analyze the forces acting on the blocks at the top of the loop to ensure they remain on the track. The discussion emphasizes the need to calculate the velocity at the bottom of the loop before the collision occurs. Understanding these dynamics is crucial for solving the problem effectively.
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Homework Statement


A block of mass m slides along a frictionless track with speed vm. It collides with a stationarty block of mass M. Find an expression for the minimum value of vm that will allow the second block to circle the loop the loop without falling off if the collision is perfect inelastic.


Homework Equations


Uinitial+Kinitial=Ufinal+Kfinal
U=mgh
K=1/2mv^2

The Attempt at a Solution


Since this is a frictionless track, there is no initial kinetic energy, but that is all i really can figure out i am completely lost someone please help!
 

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It is easier to consider this problem backwards: At the top of the loop, the masses are supposed to stay in their track. Which forces act on them? How can they stay in the track, and which velocity do they need?

The masses come from the bottom of the loop. What was their velocity there?

And afterwards, consider the collision.
 
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