# MCAT Physics Question

## Homework Statement

Two identical molecules, A and B, move with the same horizontal velocities but opposite vertical velocities. Which of the following is always NOT true after they collide:

A - the sum of kinetic energy before collision is less than the sum after
B - the sum of kinetic energy before collision is greater than the sum after
C - molecule A will have greater momentum after the collision than molecule B
D - molecule A will have greater vertical velocity than molecule B

## The Attempt at a Solution

Since they don't mention if the collision is elastic or inelastic, either A or B can be true. But I can't distinguish between C and D.

## The Attempt at a Solution

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I tried picking random numbers and doing it...

So if the horizontal velocities of the two molecules are 4, and the vertical velocity for A is -3 and for B +3

Then after they collide, momentum has to be conserved - so that would mean... after the collision, the horizontal velocities have to add up to 8 and the vertical velocities have to add up to 0 - which means that A cannot have a greater vertical velocity than B (but it can have a greater horizontal velocity)... so D could be the answer... is my logic correct?

But why is C possible?

For C... since both molecules have the same velocity and mass before the collision... the momentum for each molecule should be the same before and after the collision right? So I don't understand why C is possible

Answer C and D say the same thing. If molecule A can have a greater velocity than B this implies molecule A can have a greater momentum than B because both molecules have the same mass, if magnitudes of velocities are considered (speed). What may not be conserved is kinetic energy. So, where does the loss in kinetic energy go if the collision has an inelastic nature? Now, does it make sense that the sum of kinetic energy before the collision is less than after the collision? Where would that energy come from?

That's a good question - since it doesn't mention the collision is elastic, kinetic energy doesn't have to be conserved - the extra kinetic energy could come from numerous places - but the basic point is kinetic energy is not conserved

OK. So, kinetic energy is not conserved when an inelastic nature exists. The collision can be considered a closed system containing the two molecules. Since kinetic energy is not conserved with inelastic collisions, the initial total kinetic energy will not equal the final total kinetic energy of the system. With inelastic collisions a fraction of the initial kinetic energy is transformed into possible combinations of thermal, acoustic and deformation energies. Therefore, the final kinetic energy for this type of collision is always less then the initial. In a closed system like this how could the final kinetic energy be greater than the initial kinetic energy?

I have no idea - but the back of the book answer is D - any ideas as to why would be very helpful

This can be viewed as a one dimensional collision problem because the horizontal velocities are equal. View it as two molecules traveling in a car at a constant speed in the x direction. An observer in the car only sees the molecules moving in the y direction with opposite velocities. The total initial momentum in the y direction is zero and momentum is conserved. Therefore, the final total momentum is zero. If the collision is perfectly elastic then the relative velocity of approach before collision is equal to the relative velocity of the separation after collision. So,

vAf = vBi and vBf = vAi

If the collision is completely inelastic, the momentum equation is

mvAi - mvBi = (m + m)vf

0 = vf

Since these are the extremes the velocity of molecule A cannot be greater than the velocity of molecule B.

I'm skeptical of Choice A not being an answer because energy cannot be gained after a collision unless some outside source is introduced.