Physics momentum, speed, acceleration and GPE multi-choice question

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#1
This is the question:

Two unpowered toy cars, P and Q, are released from rest from X and travel down the track to Y. Car P has twice the mass of car Q. There is negligible friction. What quantity is the same for car P and car Q?

a) the gravitational potential at X
b) the accelerating force at X
c) the velocity when they arrive at Y
d) the momentum when they arrive at Y

I initially thought that the answer was b (the accelerating force at X) but then found out that the answer was c (the velocity). Could someone please explain how the answer is c because I'm not sure how to explain it. Thanks.
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6 months ago
#2
Have you copied out the question correctly?
Should it have read 'gravitational potential energy'?
I say this, because the gravitational potential at the point X is the same, it depends only on position in the field. However, the gravitational potential energy of the cars will be mgh and as they have different mass, m, the mgh will be different.
Because we are neglecting friction, the way the cars move down the slope is similar to how they behave in freefall.
As they lose PE they gain KE. At the bottom they both have the same speed, just as if they had fallen freely.
Their loss in potential energy, mgh, is equal to the KE they have gained 0.5mv2
The m cancels out and the velocity at the bottom just depends on h and g. g is a constant and h is the same at the same height (X).
The accelerating force will be different because it will depend on m, the same way that the cars weight depends on its mass.
Last edited by Stonebridge; 6 months ago
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