In solving my physics problems, I often end up with two equations for the same thing, they both seem right to me, and yet, it seems, they both can't be right.(adsbygoogle = window.adsbygoogle || []).push({});

I thought I would ask about this here.

I'm solving a problem which involves a box in the front of a railroad car. There is initially no motion, then the car starts to accelerate. I am asked to find various things about the box at the point when it hits the back of the car.

I started by trying to find the acceleration of the box. I get that from the kinetic friction:

fk = ma, or umg = ma, so a = ug, where u is the coefficient of kinetic friction.

With respect to the railroad car, we have

a - A = ug - A, where A is the accleration of the railroad car. So far, so good, I think. Now this is where my problems start.

If the distance the box travels backwards in the railroad car is l, then the time it takes for the box to contact the back of the railroad car is the same as it takes the car to advance l, so

l = At^2/2, and t = sqrt(2l/A).

So the velocity of the box, relative to the car, should be

v = (ug - A)sqrt(2l/A)

Of course, you can also use v^2 = 2as to do the same thing. I tried that:

v^2 = 2l(ug - A), so v = sqrt(2l(ug-A))

As far as I can tell, these aren't equivalent expressions, mathematically, for the same quantities, but I think my reasoning is sound in both cases.

This happens to me ALL the time. Can someone help me figure out which one of these is right?

Thanks,

Dorothy

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# Can both of these equations be right?

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