# Loops the loop! need help

pretty sure fc is negative also R is negative but W is positive. so... -Fc = -R + W or.. sign conversion or wtv makes it Fc = R - W i think..

PhanthomJay
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This is getting a bit mixed up, partly because the problem statement is a lttle unclear. It says nothing about constant speed , nor even if it's in a vertical circle with constant radius. So one can only make assumptions as to what is happening at the top of the loop. But anyway, I haven't yet seen anyone calculate the radius of the loop at the bottom of the path, nor the centripetal acceleration at the bottom of the loop,nor the net centripetal force at the bottom. Takers, anyone? Only after solving that can you address what might be happening at the top, with assumptions of constant speed and constant radius. The normal force at the bottom is 5mg (given); it is less than that at the top.

Fc = R - W

Therefore mv^2r/r = 5mg - mg

So, mv^2/r = 4mg, mass cancles.

v^2/r = 4g, r = v^2/4g

so (800/3.6)^2 / (4*9.8) = r , so r = ~1260m. ??

pretty sure fc is negative also R is negative but W is positive. so... -Fc = -R + W or.. sign conversion or wtv makes it Fc = R - W i think..

thats for bottom ;D

PhanthomJay
Homework Helper
Gold Member
Fc = R - W

Therefore mv^2r/r = 5mg - mg

So, mv^2/r = 4mg, mass cancles.

v^2/r = 4g, r = v^2/4g

so (800/3.6)^2 / (4*9.8) = r , so r = ~1260m. ??
You are correct that the net centripetal force at the bottom is 4mg, and the centripetal acceleration at the at the bottom is 4g. Now we already established (given) that v = 720 km/hr = 200m/s. So what's that 800/3.6 for the v value?

Oops. there is an identical question to this, forgot different Velocity. so we would substitute 200ms into it instead of (800/3.6) so we'd end up getting.. ~1020m :)

PhanthomJay
Homework Helper
Gold Member
Oops. there is an identical question to this, forgot different Velocity. so we would substitute 200ms into it instead of (800/3.6) so we'd end up getting.. ~1020m :)
Now you've got it! I'll leave it up you as an academic exercise if you what to assume something to see what may be happening at the top of the loop. Note that in more typical loop the loop problems, like yoyos in a vertcal circle , or loop the loop roller coasters , the speed is far from constant, so don't take this problem as a typical example of vertcal circular motion problems.