- #1
radagast_
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Hello!
http://img151.imageshack.us/img151/6571/cques1vd5.gif
A particle with mass m is thrown in lateral speed V_0 inside a hollow half-ball with radius R. At the beginning of it's motion the ball has an angle of \theta_0 from the perpendicular.
The gravitational force will pull the particle toward the center of the ball, while the centrifugal force will push it outwards.
Calculate the speed V_0, as a function of \theta_0, needed for the particle to reach the top of the half-ball in the peek of its motion.
Important! there's no string attached to the ball. The line on the image just indicates the radius.
\overline J=m\overline r \times \overline v
\overline \omega=\overline{ \omega_0} + \overline\alpha t
Well, the problem is I don't understand the forces involved.
I know there some sort of J_0 here, because there's an \overline r and a \overline v. I can also draw a forces equation. Then there's the Normal force against mg and centrifugal force (btw - can I use the centripetal force instead?), but I don't quite know how to combine the two - F and J - together.
Thank you.
[edit]
I thought of something: there are three forces: N, mg, \frac{mv^2}{R}.
also, I can do something like this: \Delta J = J_{end}-J_{start}, and J_{end}=0, because on the peak of the motions happens when v=0. also, J_{start}=mv_0R(sin\theta+cos\theta).
and also \frac{dJ}{dt}=r \times F
so if I only knew how to play the forces right, I would have it.
Is it correct? if so, how do I know the force equation?
http://img151.imageshack.us/img151/6571/cques1vd5.gif
Homework Statement
A particle with mass m is thrown in lateral speed V_0 inside a hollow half-ball with radius R. At the beginning of it's motion the ball has an angle of \theta_0 from the perpendicular.
The gravitational force will pull the particle toward the center of the ball, while the centrifugal force will push it outwards.
Calculate the speed V_0, as a function of \theta_0, needed for the particle to reach the top of the half-ball in the peek of its motion.
Important! there's no string attached to the ball. The line on the image just indicates the radius.
Homework Equations
\overline J=m\overline r \times \overline v
\overline \omega=\overline{ \omega_0} + \overline\alpha t
The Attempt at a Solution
Well, the problem is I don't understand the forces involved.
I know there some sort of J_0 here, because there's an \overline r and a \overline v. I can also draw a forces equation. Then there's the Normal force against mg and centrifugal force (btw - can I use the centripetal force instead?), but I don't quite know how to combine the two - F and J - together.
Thank you.
[edit]
I thought of something: there are three forces: N, mg, \frac{mv^2}{R}.
also, I can do something like this: \Delta J = J_{end}-J_{start}, and J_{end}=0, because on the peak of the motions happens when v=0. also, J_{start}=mv_0R(sin\theta+cos\theta).
and also \frac{dJ}{dt}=r \times F
so if I only knew how to play the forces right, I would have it.
Is it correct? if so, how do I know the force equation?
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