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A block with mass m, originally at rest slides downward on a
curvilinear surface given by y = (9x)^1/2 and r = 9cot(angle)
cos(angle). This is a parabola on its side. Does the block leaves
the surface before reaching the ground (y = 0)?
What is the minimum value for n in such way that the block will
leave the surface? (y = (nx)^1/2)
The first thing I noticed is that, in my opinion, you cannot use
centripetal dynamics.
Two questions:
1. Is this an original problem? I highly doubt it (There is nothing
new under the Sun) but I have never seen this type of problem before.
2. Is it solvable, even with simple calculus? Is it solvable algebraically?
3. Are there other simple curves where this type of problem could be solved?