Maximizing Sand Pulled: Angle & Weight

[coffeebird]

Homework Statement

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 1220N. The coefficient of static friction between the box and the floor is 0.24. (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?

Homework Equations

The Attempt at a Solution

dm/dθ= (-F/a)cosθ...

 

[PhanthomJay]

Before the object can accelerate, it first has to overcome static friction in the equilibrium condition(a =0). m is maximized when dm/dθ = ?. Try a free body diagram to identify forces acting, and use Newton 1 in the y direction , and Newton 1 in the x direction at the limiting value of the static friction force.