Solve Strange Problem: Beginner's Guide

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Can someone tell me how to do this problem? I Don't even know where to begin.
 
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  • Screenshot of MasteringPhysics Problem 5.70 showing a ball on a parabolic track y = x^2 with a horizontal scale from -.5 m to .5 m, followed by Part A and Part B answer entry boxes.
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Begin with F=m*a.
You should use that, and the fact that the resultant of that force and of m*g is along the normal to the surface in the equilibrium position.
 
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Consider a simpler problem first: The ball on block with a constant incline. Assume the block is accelerated towards the +x direction and that the ball is not moving vertically on the block.

The ball will experience two forces: Its weight and a normal force coming from the incline [itex]W,\ N[/itex] . Assume the incline is at an angle [itex]\theta[/itex] w.r.t. the horizontal. What can you say that the acceleration will be given by in such a situation?
 
Can you set up the force equations in the x- and y-directions using Newton's second law?

That is: "The sum of the force components on an object in the x (or y) direction is equal to its mass times its acceleration in the x (or y) direction"
 
Thanks for the help guys. I still couldn't get it, though. I'll give it another crack soon for test preparation.