Loop-d-loop Physics Question

[dmplz707]

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Hey guys I have s question on this loop-d-loop problem...

A 1,000 kg roller coaster car completed a loop-d-loop on its track. Is the normal force acting on the car by the track greater at the top or bottom of the loop-d-loop? By how much (answer in terms of m, v, r, and g)?

So I'm having trouble at the top of the loop-d-loop where I just can't seem to get the signs to agree. I have set negative going vertically down and positive going vertically up...

Bottom

mv^2 / r = N - mg

N = mg + mv^2 / r

Top

mv^2 / r = - N - mg

N = - mg - mv^2 / r


That's actually what I have right now but the top should be;

N = mv^2 / r - mg

Did I do something? How come the signs aren't matching? Thanks guys.

 

[computernerd225]

Why do you have -N for the normal force at the top? You should be using N1 and N2 as the normal forces will be different. Just use positive N (as the answer will be negative anyways if you are using real numbers) and add mg instead of subtracting (the forces are in the same direction).

top: m*(v^2/r) = N2 + mg

N2 = mv^2 / r - mg

Hope this helps, I think my physics is a bit rusty.

 

[dmplz707]

Thanks guys. I was tripping out but I forgot to take into account the sign of the acceleration. Thanks again!