Why Is Calculating Normal Force at the Top of a Rollercoaster Tricky?

[vorcil]

http://img7.imageshack.us/img7/9297/masteringphysicsq1.jpg - screenshot of the question



2.
ok the first question asks for the normal force at the top, I'm pretty sure the normal force at the top is (mv^2)/r - mg = ( (51kg * v^2 ) / 18m) - mg

to get the velocity i went 2*pi*18/5.5 which is 20.56 ms^-1

stuck that in mv^2/r -mg = 697.8N, AND I GOT IT WRONG!?
is there something I'm missing?

i did the same thing for the bottom except added mg and got it wrong,

 

[Doc Al]

You are given the diameter, not the radius.

 

[vorcil]

You are given the diameter, not the radius.

OMFG LOL
cheers mate,

 

[vorcil]

I got the last one correct aswell,

I know at the top the normal force must excel the mg,
so at the point the mg > normal then it will start to fall

so if
mg > mv^2/r ==
51*9.8 = (m*((2*pi*r)/t)^2)/r ==
51*9.8 * r = m*((2*pi*r)/t)^2 ==
squareroot (51*9.8*r) = m*((2*pi*r)/t
longest time for mg to equal Normal force == (m*(2*pi*r))/(51*9.8*r)
and i got 6 seconds which was right XD

 

[Doc Al]

I know at the top the normal force must excel the mg,
so at the point the mg > normal then it will start to fall

Careful here. The riders begin to fall when the normal force goes to zero, not when it drops below mg.

so if
mg > mv^2/r ==

That's what you want.

(mv^2/r is the centripetal force, not the normal force.)

 

[vorcil]

Careful here. The riders begin to fall when the normal force goes to zero, not when it drops below mg.

That's what you want.

(mv^2/r is the centripetal force, not the normal force.)

So it's the centripetal force that has to be greater than mg?

i get it, but isn't it strange how the centripetal force is acting towards the center, i would've thought because they're going in the same direction it'd make it fall even more
but i know what you mean because it's hitting the side of the rails making it go down and around XD

 

[Doc Al]

Centripetal force always acts toward the center, by the nature of circular motion. The word "centripetal" just means "toward the center". But don't think of centripetal force as if it were a separate force, like gravity; instead, it's just a way to describe how the net force must act in circular motion.

At the top of the rollercoaster, the centripetal force is provided by two real forces: The normal force and gravity. The faster the coaster moves, the greater the centripetal force required, thus the greater the normal force that the track must exert to keep the car from flying off into space. If the coaster slows down, the normal force required is less. The slowest it can go and still maintain contact is just at the point where the normal force goes to zero. That means that the only force providing the centripetal force is gravity (mg). If the coaster goes any slower, gravity pulls it off the track and into the air.

Make sense?