An initially stationary box of sand is to be pulled across a floor by means of a

Question

An initially stationary box of sand is to be pulled across a floor by means of a cable in which the tension should not exceed 846N. The coefficient of static friction between the box and the floor is 0.37. (a) What should be the angle between the cable and the horizontal in order to pull the greatest possible amount of sand, and (b) What is the weight of the sand and box in that situation?

Explanation / Answer

let the angle be O N=mg-846sinO (m=weight of sand box) f=(mg-846*sinO)*.37 horizontal tension force=846cosO =>equating both we get .37mg=(.37*846sinO+846cosO) for m to be maximum .37sinO+cosO has to be max diiferentiate with erspect to O .37cosO-sinO=0 =>tanO=.37 O=20.3 degrees b)putting these values we get .37mg=846(.37*.34+.93) =>m=241kg Ans.

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