Question

A block of mass 200 kg is being pulled up by men on an inclimed plane at angle of 45 degree the coefficient of static friction is 0.5 each man can only apply maximum force of 500N. Calculate the number of men required fir the block to just start moving up the plane

Answer 1

answer : 5

mass of block, M = 200kg

inclination of plane , θ = 45°

coefficient of static friction , μ = 0.5

each man can only apply maximum force, F = 500N.

free body is shown in figure. block just starts moving up the plane. so, frictional force acting downward along plane.

at equilibrium,

weight of block along plane + frictional = Tension in string

or, Mgsinθ + fr = T

or, Mgsinθ + μ (Mgcosθ) = T

now putting values of M, g , μ and θ

so, 200 × 10 × sin45° + 0.5 × 200 × 10 × cos45° = T

or, 1000√2 + 500√2 = T

or, 1500√2 = 2121.32 = T

number of men is required for the block to just start moving up = T/F = 2121.32/500 = 4.24

we know, number of men can't be fractional xD, so, number of men required = 5