Answer:

The weight of the block of wood in the illustration is 96.5. The coefficient of static friction between block of wood and vertical wall is 0.45.

a) What minimum force is required to stop the bloc from sliding down the wall?

b) What force is required tot start the bloc moving up the wall?

In both cases the normal force between the block and the wall is due to the horizontal component of the applied force F:

FN=Fsin35

The only difference between question (a) and question (b) is the direction of the friction force.

a) Impending motion downward

For impending motion downward, the direction of the friction force is up.

ΣFy=0

Ffric+Fcos35−W=0

or

μFN+Fcos35−W=0

or

μ(Fsin35)+Fcos35−W=0

or

F[(μsin35)+cos35]=W

or

F=W[(μsin35)+cos35]

a) Impending motion upward

For impending motion up, the direction of the friction force is down.

ΣFy=0

−Ffric+Fcos35−W=0

or

−μFN+Fcos35−W=0

or

−μ(Fsin35)+Fcos35−W=0

or

F[−μsin35+cos35]=W

or

F=W[cos35−μ(sin35)]