# Uniform circular motion car problem

1. Oct 11, 2007

### S[e^x]=f(u)^n

1. The problem statement, all variables and given/known data
a cart with a person in passes over a circular arch at a constant speed v who's radius is r. Does the maximum speed the cart can go without leaving the tracks depend on the mass of the person, the mass of the cart, both, or neither?

2. Relevant equations
Fg=mg -Gravitational Force
Fc=(mv^2)/2r? -Centripetal force
Fn=? -Normal force

3. The attempt at a solution
Fc=Fg-Fn
i honestly don't know where to go from here? can anyone offer any hints... i need to figure it out by tomorrow afternoon. my gut says it depends on neither, but from math i've fiddled around with it seems to indicate it depends on both

2. Oct 11, 2007

### PhanthomJay

that "2" in the denominator of your Fc equation doesn't belong there. Your equation Fc = Fg -Fn is good.
What is the value of Fn just as the cart would leave the tracks?

3. Oct 12, 2007

### S[e^x]=f(u)^n

sorry about the 2, i don't know why i put it there. anyway Fn would be 0 on the cart, but so would the Fn for the person inside... wouldn't it? in which case the cart would leave the tracks at the same speed regardless of whether there was a person in there?... but is it still dependent on the weight of the car?

4. Oct 12, 2007

### Staff: Mentor

Well, weight (mg) is pulling down while the centrifugal force (mv2/r) would cause the cart to go tangent to the track. For the cart to stay on the track those two forces must be equal.

Set the forces equal and see what happens with respect to mass.

5. Oct 12, 2007

### nrqed

what is special when the car is driven at the maximum speed so that it is just about to lose contact with the ground is that the normal force is zero. Isolate for the speed and you will have your answer. (btw, you should have mv^2/r, not mv^2/2r)

6. Oct 12, 2007

### S[e^x]=f(u)^n

thanks, from what i can figure out the velocity at which the cart(regardless of mass) leaves the tracks is dependent solely on the square root of the radius. which sounds about right to me

7. Oct 12, 2007

### nrqed

correct. (and it depends on the acceleration due to gravity...the max speed on th emoon would be different ;-) )

8. Oct 12, 2007

thanks!