- #1
mamadou
- 24
- 1
Homework Statement
An empty ball , of mass m moment of inertia I = (2m.r²)/3, is rolling across the path shown below :
there is friction fr from A to C .
r is the radius of the ball , and R is the radius of the circular part within the path .
what would be the minimal height h , so that the ball can make a complete lap in the loop (the circular part) ?
Homework Equations
∑F = m.a
∑τ = I . α = r.I.α / where α is the angular acceleration , I the moment of inertia , and r the radius .
The Attempt at a Solution
after some computations I've found :
[tex]a_{T} = \frac{g.\sin(\alpha)}{\frac{2}{3}r^{2}-1}~~[/tex] ( a_T ; is the translational acceleration)
[tex]f_{r} = \frac{2m.g.\sin(\alpha).r^{2}}{2r^{2}-3}[/tex]
I know that the ball must roll on a distance of 2πR( the perimeter of the loop). But I can't figure out how to link between the acceleration and this distance ?[/B]
picture link : https://i.imgsafe.org/38bb5dc5ca.png