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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 |
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Answer» 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 |
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