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Satvik Pandey
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Homework Statement
A solid spherical ball is placed carefully on the edge of a table in the position shown in the figure. The coefficient of static friction between the ball and the edge of the table is 0.5 . It is then given a very slight push. It begins to fall off the table.
Find the angle (in degrees)(with vertical) turned by the ball before it slips.
Homework Equations
3. The attempt at questionI have came up with some equations. Let ##\theta## be the angle(with vertical) at which the sphere begins to slip.
By conservation of energy
##mgr-mgrcos\theta =\frac { 1 }{ 2 } { I }_{ 0 }{ \omega }^{ 2 }##
As ##v=r \omega##
So ##g(1-cos\theta )=\frac { 7 }{ 10 } \frac { { v }^{ 2 } }{ r } ##
By finding torque about the contact point
##mgsin\theta r=\frac { 7 }{ 10 } m{ r }^{ 2 }\alpha ##
As ##a=r \alpha##
So ##\frac { 5gsin\theta }{ 7 } =a##
Also from FBD of the block
##mgcos\theta -N=m\frac { { v }^{ 2 } }{ r } ##
and ##\\ mgsin\theta -\mu N=ma##
I don't know if these equations are right. Please help.
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