Impulse, momentum and efficiency to find height formula
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1. The problem statement, all variables and given/known data A ramp system is set up. Due to friction the ramp has an efficiency of 82%. Two cars of equal mass are allowed to collide and car 1 starts from rest at height h1. The two stick together and coast to a height of h2. Derive a formula relating h1 to h2. 2. Relevant equations I=Δp, p=m*v, eff=(output/input)*100%, GPE=mgh, 3. The attempt at a solution Unfortunately, I cannot figure out almost anything based on this question. Even my friend's father, who is an engineer, could not understand. Just looking for some good help if any one is available. 
Re: Impulse, momentum and efficiency to find height formula
First things first, what is the speed car 1 just before impact? It's kinetic energy is not mgh_1 but some fraction of that.

Re: Impulse, momentum and efficiency to find height formula
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What is the definition of efficiency to apply? Final system energy over initial system energy? Final velocity over ideal velocity? Something else? * Doctor Who 
Re: Impulse, momentum and efficiency to find height formula
I would calculate kinetic energy (it is not the same as the potential energy, since the efficiency is less than 100%). Then, I would find speed, and later calculate the speed after the inelastic collision. Then, I would use conservation of energy.

Re: Impulse, momentum and efficiency to find height formula
Gneill, I think that efficiency here refers to energy; in other words, only 82% initially available energy is useful, and the other 18% is converted to other forms of energy.

Re: Impulse, momentum and efficiency to find height formula
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Perhaps the OP has been given a particular working definition of efficiency that can be applied here? 
Re: Impulse, momentum and efficiency to find height formula
For this question I have been told to use Input/Output for efficiency, if that helps at all.

Re: Impulse, momentum and efficiency to find height formula
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In MANY cases, the situation is idealised by assuming there is no friction. In this case it looks like a more representative, but equally random, assumption has been made and so when moving up and/or down this slope, instead of 100% of the PE converting to KE on the way down the hill, only 82% of the PE ends up as KE. I would assume that after the collision, only 82% of the KE after collision becomes the PE when they stop. 
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