Answer:
83.26 N
Step-by-step explanation:
Let F be the horizontal force applied to the block . This has two components:
and


The weight of the block is mg acting vertically downward.
mg = 4 x 9.8 = 39.2 N
This can be decomposed into 2 components - one parallel to the plane acting downward opposite to
and the other perpendicular to the plane and acting in the same direction as

The two components of mg are


In addition we have the friction component that acts on the perpendicular combined force
Total perpendicular force =

This perpendicular force also experiences friction with a coefficient of 0.7 so net perpendicular force =

Total Force acting parallel to the plane
=

So we get

Or

Plugging in values for sin and cos θ and mg we get
F x 0.866 = 39.2 x 0.5 + 0.7(F x 0.5 + 39.2 x 0.866)
==> 0.866F = 19.6 + 0.35F + 23.76
==> 0.866F = 0.35F + 42.96
==> 0.866F - 0.35F = 42.96
==> F(0.866 - 0.35) = 42.96
==> 0.516F = 42.96
==> F = 42.96/0.516 =
==> F ≈ 83.26 N