A bar of mass m is pulled by means of a thread up an inclined plane forming an angle α with the horizontal (fig.). The coefficient of friction is equal to k. Find the angle β which the thread must form with the inclined plane for the tension of the thread to be minimum. What is it equal to?
Text Solution
Verified by ExpertsCHECK THE SOLUTION.
tan β = k; T min = mg (sin α + k cos α ) / 
.
Sol. For limiting friction
N + T sin β = mg cos α
⇒ N = mg cos α – T sin β ——(i)
and, Tcos β = mg sin α + f
= mg sin α + k (mg cos α – T sin β ) (from (i))
⇒ T (cos β + k sin β ) = mg sin α + k mg cos α
⇒ T = 
for minimum T, cos β + k sin β should be maximum
Let y = cos β + k sin β
= –sin β + k cos β = 0
⇒ tan β = k
∴ T min = 
= 
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