What is the minimum speed the car must have at the top?

[Epsillon]

Homework Statement

A roller coaster loop has a radius of 12m. If the passengers in a car are not to fall out at the top of the loop, what is the minimum speed the car must have at the top?

The Attempt at a Solution

Alright I think I got the right answer but I do not completely understand the question.

so what i did was

I went Fc=Fg (but why??)

g is 9.8
mg=mv^2/r

g=v^2/r
v=11

But I don't get why the MINIMUM ac has to be g for them not to fall off.

 

[phyzmatix]

But I don't get why the MINIMUM ac has to be g for them not to fall off.

If the acceleration is less than g, then the force on passengers due to the acceleration of the roller coaster will be less than that on the passengers due to gravity and gravity will "win", i.e. the passengers will fall.

Therefore, if the minimum acceleration is equal to g the force will allow for passengers to remain in their cars (i.e. the force due to gravity won't be able to "overcome" the force due to the centripetal acceleration) and an acceleration greater than g will obviously have the same effect.

I hope this makes sense to you. I'm not that hot at explaining, so perhaps someone else can put it better?

 

[Epsillon]

OHHH so this questions is defining falling as the car not going around the cirlcle.

I thaought it means that they go weightless.

 

[phyzmatix]

OHHH so this questions is defining falling as the car not going around the cirlcle.

I thaought it means that they go weightless.

Think about what you said...remember that Weight = Mass x Gravitational Acceleration (g) so, when the centripetal acceleration of the car equals g, the passengers subject to this force (due to the centripetal acceleration) are in effect "weightless", which is why they don't fall (the force due to the centripetal acceleration cancels the force due to gravity).

I can't get latex to work, but the vectors, for this case is:

Weight = mass x (centripetal acceleration + gravitational acceleration)

at the top of the loop this means that, with centripetal acceleration = g and g and centripetal acceleration directed opposite each other

Weight = mass x 0 = 0

Make sense?