Problema Solution
The load that can be supported by a rectangular beam varies jointly as the width of the beam and the square of its height , and inversely as the length of the beam. A beam 12 feet long, with a width of 6 inches and a height of 4 inches can support a maximum load of 800 pounds. If a similar board has a width of 9 inches and a height of 7 inches, how long must it be to support 1200 pounds?
Answer provided by our tutors
let
m = the weighed of the load
w = the width of the beam
h = the height of the beam
l = the length of the beam
m = C*w*h^2/l, where C is constant
l = 12 ft
w = 6 in
h = 4 in
m = 800 lbs
that is if we plug these values into m = C*w*h^2/l we have:
800 = C*6*4^2/12
by solving we find:
C = 100
click here to see the step by step solution of the equation:
m = 100*w*h^2/l
w = 9 in
h = 7 in
m = 1,200 lbs
l = ?
1200 = 100*9*7^2/l
by solving for l we find:
l = 36.75 in
click here to see the step by step solution of the equation:
the length of the beam must be 36.75 in.