Solving Two Problems: 500 kg Cart on a 9 m Loop-the-Loop

[jromega3]

Homework Statement

The two problems below are related to a cart of mass M = 500 kg going around a circular loop-the-loop of radius R = 9 m, as shown in the figures. Assume that friction can be ignored. Also assume that, in order for the cart to negotiate the loop safely, the normal force exerted by the track on the cart at the top of the loop must be at least equal to 0.4 times the weight of the cart. (Note: This is different from the conditions needed to "just negotiate" the loop.) You may treat the cart as a point particle.

Homework Equations

The Attempt at a Solution

 

[djeitnstine]

What are you solving for and where is your attempt?