One more physics question for the night?

Question

The weight of the block is 80 N. The coefficient of static friction between the block and the vertical wall is .60. a) What minimum force is required to prevent the block from sliding down the wall? and b) What minimum force F is required to start the block moving up the wall?


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Sorry if the picture doesn't make a lot of sense. It shows the block on the wall, and force being applied at an angle of 40 degrees.

Answer 1

Good Evening.

a) Hold the block.

down force (weight) = friction force + Fv

Where friction force = coefficient of friction times the normal force (or the normal to the wall component of the applied force F). So we have
Fv= Fcos(40)
W=uFsin(40) + Fcos(40)
F=W/(usin(40) + cos(40))

F=80 /(.60 sin(40)+cos(40)=70N

b) To slide the block up

The force up = weight + force of fiction

F cos(40) = W + u F sin(40)

F (cos(40) - u sin(40))=mg
F=W/(cos(40) - u sin(40))
F=80(/(cos(40) - 0.60sin(40))=
F=210 N

Now Good Night.

Answer 2

Assuming force F makes 40 degree with the vertical

Component of force F perpendicular to the wall= Fsin40

Component of force F parallel to the wall= Fcos40

Normal reaction R of the wall on the block =F sin40

The weight W of the block = 80 N.

The coefficient of static friction between the block and the vertical wall (mu) =0.60.

limiting friction force 'f'=coefficient of static friction (mu)*normal reaction R

f = 0.60*F sin40

When block is about to slide downward, the friction force is upwards

Upward total force=component of F parallel to wall+friction 'f'

Upward total force=Fcos40 + 0.6 F sin40

Downward total force = weight W = 80 N

As the block does not slide down,

Upward total force=Downward total force

F cos40 + 0.6 F sin40 = 80

F( cos40 + 0.6 sin40) = 80

F (0.766 +0.6*0.642) = 80

F(1.1517)= 80

F =80 / 1.1517 = 69.46 N

(a) The minimum force F required to prevent the block from sliding down the wall is 69.46 N
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(b) When the block is to move up friction force acts down (as friction opposes tendency of motion)

Upward total force=Fcos40

Downward total force = weight W+friction'f' = 80 +0.6 F sin40

Upward total force=Downward total force

F cos40 = 0.6 F sin40 + 80

F( cos40 - 0.6 sin40) = 80

F (0.766 - 0.6*0.642)= 80

F (0.3804) = 80

F = 80 /0.3804= 210.3 N

(b) The minimum force F required to start the block moving up the wall is 210.3 N