The Maximum Weight

Question

The Maximum weight that a rectangular beam can support varies jointly as its width and the square of its height and inversely as its length. If a beam 1/3 foot wide, 1/4 foot high, and 17 feet long can support 10 tons, Find how much a similar beam can support if the beam is 3/4 foot wide, 1/3 foot high, and 13 feet long. 

Answer 1

 

Hi again, Theresa -- since the 2nd beam is fatter and shorter, we can expect GREATER load support ... width bigger 9/4x ... ht bigger 4/3x ... h^2 bigger 16/9x ... L smaller 13/17 => bigger load by 17/13 ... expect bigger load of 9/4(16/9)17/13 ...  4(17/13) ... 68/13 ...

5 1/4x ==> 52.5 tons :)

Answer 2

Maximum weight =k W*H^2/L, where k is a constant.

10 = k(1/3)(1/4)^2/17 = k/816......(1)

x = k(3/4)(1/3)^2/13 = k/156 ......(2)

(2)/(1): x/10 = 816/156 = 68/13

x = 680/13 = 52.31 tons <==Answer