A 200 lb box is setting on an inclined plane which has an angle of 30 degrees. The coefficient of static friction in this case is 0.3.
a) What is the force acting normal to the surface of the plane?
b) What is the component of the force of gravity acting down the plane?
c) What is the maximum friction force acting to keep the box from moving?
d) What force is needed to start the box moving up the plane?
e) What force is needed to start the box moving down the plane?
diagram in comments
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here , for the equilibrium of the block
let the force normal to surface is N
N = W * cos(30)
N = 200 * cos(30)
N = 173.2 lb
the force acting normal to surface is 173.2 lbf
component of gravity down the plane = W * sin(30)
component of gravity down the plane = 200 * sin(30)
component of gravity down the plane = 100 lbf
the component of gravity down the plane is 100 lbf
maximum friction force = u * N
maximum friction force = 0.30 * 173.2
maximum friction force = 52 lbf
the maximum friction force is 52 lbf
let the force needed is F
for the block to move upwards
F - W * sin(30) - friction force = 0
F - 100 - 52 = 0
F = 152 lbf
the minimum force needed to move the block up the plane is 152 lbf
for the block to move downwards
as gravity component down the plane is greater than friction
the block will start moving downwards with out any force