S cornwell asked 1 year ago
The coefficients of friction between the block and the rail are μN = 0.30 and μk = 0.25. Knowing that θ =65° determine the smallest value of P required (a) to start the block up the rail, (b) to keep it from moving down.
Sazid Ahmad answered 1 year ago
Step: 1
(a)
Draw the free body diagram of the block.
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Step: 2
Assume that the force in the positive x-direction is positive.
Apply the equilibrium condition,
…… (1)
Assume that the force in the positive y-direction is positive.
Apply the equilibrium condition,
…… (2)
Step: 3
The maximum value of frictional force,
As the block is starting to move up the rail (impending motion), frictional force:
…… (3)
Substitute the value of N in equation (1) and solve.
…… (4)
Substitute the value of P and N in equation (2) and solve.
Substitute the value of F in equation (4) and solve.
Therefore, the smallest value of the force P required to start the block moving up the rail is 
.
Step: 4
(b)
Draw the free body diagram of the block when it will try to slip down.
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Step: 5
Take the condition of equilibrium.
Assume that the force in the positive x-direction is positive.
Apply the equilibrium condition. 
…… (5)
Step: 6
Assume that the force in the positive y-direction is positive.
Apply the equilibrium condition,
…… (6)
The maximum value of frictional force,
As the block needs to be kept from moving down, frictional force,
…… (7)
Step: 7
Substitute the value of N in equation (5) and solve.
…… (8)
Substitute the value of P and N in equation (6) and solve.
Substitute the value of F in equation (8) and solve.
Therefore, the smallest value of force P required to keep the block from moving down is 
.