The load that can be supported by a rectangular been varies

The load that can be supported by a rectangular been varies jointly as the width of the beam and the square of its height inversely as the length of the beam. A beam 13 feet long with of 4 inches and a height of 6 inches can support a maximum lead of 800 pounds. If a similar boards has a width of 8 inches and a height of 7 inches, how long must it be to support 1300 pounds?

Solution

Load support can be expressed as

F = k*h^2*w/L

Now it\'s given that

F1 = 800 N

L = 13 ft

w = 4 in = 0.33 ift

h = 6 in = 0.5 ft

So,

800 = k*0.5^2*0.33/13

k = 800*13/(0.5^2*0.33) = 126060.60

Now we need to find L when

w = 8 in = 0.67 ft

h = 0.7 in = 0.583 ft

F = 1300 ft

So,

1300 = 126060.60*0.67*0.583^2/L

L = 126060.60*0.583^2*0.67/1300

L = 22.08 ft