Question

A Block of mass m = 4 kg is placed over a rough inclined plane as shown in figure, The coefficient of friction between the block and plane is μ = 0.6. A force F = 10 N is applied on the block of an angle at 30°. The contact force between the block and the plane is ______ 

(A) 27.15 N 

(B) 16.32 N 

(C) 10.65 N 

(D) 32.16 N

Answer 1

Correct option: (A) 27.15 N

Explanation:

m = 4kg, μ_s = 0.6, F = 10N

N + F sin 30 = mg cos 45

N + (F / 2) = 4 × 10 × (1 / √2)

N + 5 = (40 / √2)

N = 23.28

f_s(max) = μs N

f_contact = √(f_{s max}² + N²)

= √(μ_s² N² + N²)

= N √(μ_s² + 1)

f_contact = 23.28 √(0.6² + 1)

= 27.16 N