# Circular motion - velocity of carts on a rollercoaster

1. Oct 12, 2008

### klaw25

1. The problem statement, all variables and given/known data
Six roller-coaster carts pass over the same semicircular "bump." The mass M of each cart (including passenger) and the normal force n of the track on the cart at the top of each bump are given in the figures. Rank the speeds (from largest to smallest) of the different carts as each passes over the top of the bump.
Cart #1: Normal force of 200 N, mass of 400 kg
Cart #2: Normal force of 800 N, mass of 800 kg
Cart #3: Normal force of 400 N, mass of 200 kg
Cart #4: Normal force of 400 N, mass of 100 kg
Cart #5: Normal force of 800 N, mass of 100 kg
Cart #6: Normal force of 300 N, mass of 300 kg

2. Relevant equations
F = ma
a = v^2 / R

3. The attempt at a solution
If you are supposed to find the acceleration by using F = ma, then these are the accelerations:
#1: 0.5 m/s^2
#2: 1 m/s^2
#3: 2 m/s^2
#4: 4 m/s^2
#5: 8 m/s^2
#6: 1 m/s^2
..I don't know if that's the correct initial step. I'm not sure what to do from here. The radius is not given.

2. Oct 13, 2008

### Rake-MC

Radius is not given, however they do not ask for a numerical answer, just an order of fastest speeds to slowest speeds.

At the peak of the semicircle, you are given the normal force, you are also given the mass of each cart so you can calculate the force due to gravity
When you sum up these two forces, you will have the net force (hopefully it's down or else the carts will fly off the tracks!!).

You know that:

$$F = \frac{mv^2}{r}$$

So you can re-arrange for velocity in terms of radius. Repeat for each cart, then simply rank them in order.