The strength of a rectangular beam varies jointly with its width and the square of its thickness. if a beam 4 inches wide and 2 inches thick supports 480 pounds, how much can a beam of the same material that is 3 inches wide and 1 inch thick support?

∴ S = 90 lbs

Explanation:

S = kwt²

480 lbs = k(4 in) (2 in)²

             = k (4 in) ( 4 in²)

              = k × 16 in³

∴ K =( 480 ÷ 16 ) lb/in³

    K = 30 lb/in³

When w = 3 inches and t = 1 inches:

S = (30 lb/in³) × (3 inches) × (1 in)²

  =   (30 × 3 ×1 ) lb

   = 90 lb

∴ S = 90 lbs