A block of mass m is placed on a wedge of mass 2m which rests on a rough horizontal surface . There is no friction between the block and the wedge. Find the minimum coefficient of friction so that the wedge does not move is
Answers
Answer:
Explanation:
=> Here, we can calculate the minimum coefficient of friction by using the below formula:
F = μN
Where,
F = the resistive horizontal force of friction
μ = coefficient of friction for the two surfaces
N = the normal or perpendicular force pushing the two objects together
=> Thus, net Horizontal force on the wedge, F:
F - mgsinፀcosፀ = m(a) [but m(a)= 0]
F - mgsinፀcosፀ = 0
F = mgsinፀcosፀ
F = mg sin 45° cos 45° [sin 45° = 1/√2, cos 45° = 1/√2]
F = mg * 1/√2 * 1/√2 [1/√2 * 1/√2 = 1/2]
F = mg/2
Now, the normal or perpendicular force N:
N = mgcos²ፀ + 2mg
= mgcos(45°)²+ 2mg [cos(45°)² = 1/2]
= mg/2 + 2mg
= mg + 4mg / 2
= 5mg / 2
=> Thus, the minimum coefficient of friction, μ:
F = μN
μ = F/N
= mg / 2 / 5mg / 2
= mg * 2 / 2 * 5mg
= 1/5
= 0.2