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CSS 2017 Paper of Applied Maths

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Q. No. 2. (a) A 100 Kg wooden crate rests on a wooden ramp with an adjustable angle of inclination. Draw a free body diagram of the crate. If the angle of the ramp is set to 100, find the perpendicular and parallel components of the crate’s weight to the ramp. Also find the static friction force between the crate and the ramp. At what angle will the crate just begin to slip? (coefficient of static frictions between wood block and wood surface is 0.28)

(b) A ladder having a uniform density and a mass m rests against a frictionless vertical wall at an angle of 600. The lower end rests on a flat surface where the coefficient of static friction is 0.40. A person of mass M=2m attempts to climb the ladder. What fraction of the length L of the ladder will the person have reached when the ladder begins to slip?

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