Answer 1:
Yup, it looks like everything's almost
perfect!
There's one minor detail: when you solved for
N_{2}, you switched the sign around.
That is, you
got
N_{2} = (m*g)  (N*sinθ)
while it should be
N_{2} = (N*sinθ) (m*g)
so your final answer is off by an overall minus
sign: it should be
“Up” Force = N_{2} = m*(
((v_{2}/r)*tanθ)  g )
An easy way to check the answer is by
consider
what are called limiting case:
What happens when
certain quantities go to some extreme limits?
For example, say we spin the cone faster, so
that v becomes bigger. We expect the ball to
get "wedged" in the cone much more tightly, so
that the force should become very big and
positive. But in your answer, as v gets bigger,
the force gets big and negative, which means
there was something off about it.
These sorts of things are very handy tricks
for
checking your answer, and making sure you
understood the problem.
Anyway, very nice! I like this problem.
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