A block of mass m is placed on a rough horizontal floor. A force F is applied to the block by means of a light string making an angle θ above the horizontal. The coefficient of static friction between the block and the floor is μs. (Take g=9.8m/s2.)
a. (i) For impending motion, derive an equation relating F, μs, m, g and θ.
b. (ii) Using the result of part (i), obtain an expression for F as a function of θ and hence determine the angle θ at which F is minimum.
c. (iii) For m=10kg and μs=0.50, calculate the numerical values of the optimum angle and the minimum force.