Question

3 flat blocks in the figure are positional on 37° incline and force parallel to the inclined plane is applied to middle block . the upper block is prevented from moving by a wire which attaches it to the fixed support the masses of three blocks in kg and coefficient of static friction for each three pairs of contact surface is shown . determine maximum value which force p may have before slipping take place anywhere.​

Answer 1

Explanation:

Let f

1

,f

2

,andf

3

be the frictional force between (30kg and 50kg), (50kg and 40kg), and (40kg and ground).

f

1max

=μ

1

(30g)cosθ=0.3×30×10×cos37

∘

=3×30×

5

4

=72N

f

2max

=μ

2

(50+30)gcos37

∘

=0.4×80×10×

5

4

=256N

f

3max

=μ

3

(40+50+30)gcos37

∘

=0.5×120×10×

5

4

=480N

here, f

3max

>>f

2max

+40gsinθ

Therefore slipping takes place, only for 50kg block slide and 40kg stay

P+50gsin37

∘

=f

1max

+f

2max

P+50×10×

5

3

=72+256

P=72+256−300=28N