Question

A 600 N box is held in place on the smooth bed of the dump truck by the rope AB. 

(a) If α = 25°, what is the tension in the rope? 

(b) If the rope will safely support a tension of 400 N, what is the maximum allowable value of α ?

Answer 1

The projections of the rope tension and the normal force are

The equilibrium conditions are

Substitute, and collect like terms

Solve for the unknown tension when For α  = 25°

For a tension of 400 , (600 sin α - 400) = 0. 

Solve for the unknown angleα = 400/600 

= 0.667 or α = 41.84°.