How can I determine the magnitude of the
vertical (“up”) force that the sphere exerts on
the lid, given the radius of the cone, its
tangential velocity, and the mass of the sphere
(s) (and of course, from that information, the
centripetal acceleration experienced by the
sphere)?
see figure
I have done the following calculations (shown
below) to determine the magnitude of the
vertical force, with the help of a professor
from school. We made a few assumptions about the
rotating sphere in order to simplify the
problem, but overall I think the calculations
should still approximate a real life situation.
I would like to make sure that we have not made
any errors, however. Would you guys mind looking
at it and making sure our calculations are
correct?
Thank you!
∑ FY = (– m*g) – N_{2}M + (N*sinθ)
= 0
∑ FX = (N*cosθ) = m*(v_{2}/r)
N_{2} = (m*g) – (N*sinθ)
(N*cosθ) = (m*v_{2})/r
N = (m*v_{2})/(r*cosθ)
N_{2} = (m*g) – ( ((m*v_{2})/
(r*cosθ))*sinθ )
N_{2} = (m*g) – ( ((m*v_{2})/r)
*tanθ)
N_{2} = m*(g – ((v_{2}/r)
*tanθ) )
“Up” Force = N_{2} = m*(g –
((v_{2}/r)*tanθ) )
Where v equals the tangential velocity of the
rotating cone.
