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I'm having trouble getting started on this entire problem. I've redrawn it, I'm given the mass of the cart, and the radius of the loop.. but I have absolutely no idea how I can calculate even the first part of this (minimum high h).
I'd greatly appreciate any help anyone could offer. Thank you!!

The two problems below are related to a cart of mass M = 500 kg going around a circular looptheloop of radius R = 15 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 0.6 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.
a) For this part, the cart slides down a frictionless track before encountering the loop. What is the minimum height h above the top of the loop that the cart can be released from rest in order that it safely negotiate the loop?
b) For this part, we launch the cart horizontally along a surface at the same height as the bottom of the loop by releasing it from rest from a compressed spring with spring constant k = 10000 N/m. What is the minimum amount X that the spring must be compressed in order that the cart "safely" (as defined above) negotiate the loop?
c) When the car is descending vertically (ie at a height R above the ground) in the loop, what is its speed v?
d) At the bottom of the loop, on the flat part of the track, the cart must be stopped in a distance of d = 20 m. What average retarding acceleration a is required?
I'd greatly appreciate any help anyone could offer. Thank you!!

The two problems below are related to a cart of mass M = 500 kg going around a circular looptheloop of radius R = 15 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 0.6 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.
a) For this part, the cart slides down a frictionless track before encountering the loop. What is the minimum height h above the top of the loop that the cart can be released from rest in order that it safely negotiate the loop?
b) For this part, we launch the cart horizontally along a surface at the same height as the bottom of the loop by releasing it from rest from a compressed spring with spring constant k = 10000 N/m. What is the minimum amount X that the spring must be compressed in order that the cart "safely" (as defined above) negotiate the loop?
c) When the car is descending vertically (ie at a height R above the ground) in the loop, what is its speed v?
d) At the bottom of the loop, on the flat part of the track, the cart must be stopped in a distance of d = 20 m. What average retarding acceleration a is required?
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