small block of mass m is in contact with the inner wall of a large hollow cylind
ID: 2006003 • Letter: S
Question
small block of mass m is in contact with the inner wall of a large hollow cylinder. Assume the coefficient of static friction between the object and the wall of the cylinder is ?. Initially, the cylinder is at rest, and the block is held in place by a peg supporting its weight. The cylinder starts rotating about its center axis, as shown in the figure, with an angular acceleration of ?. Determine the minimum time interval after the cylinder begins to rotate before the peg can be removed without the block sliding against the wall. (Use any variable or symbol stated above along with the following as necessary: d for the diameter of the cylinder, and g for the acceleration due to gravity.) t= ?Explanation / Answer
We have 2 forces acting on the block, force of friction f that prevents the block from sliding down and the force of gravity W forcing the block to slide.
Force of friction is
f= (m V2/R) where the component m V2/R is the centrifugal force.
m- mass of the block
V - linear speed of teh block
R- radius of the cylinder
since in terms of angular acceleration an dangular speed =t
V= R= tR we have
f= m(tR)2/R or
f=m(t)2R
Force due to gravity W is
W=mg
Now we have the block will not slide when W=f
mg=m(t)2R
then
t=(1/) (g/(R) )
Please let me know if you have any questiions.
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