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 13
feet long, with a width of 4
inches and a height of 6
inches can support a maximum load of 800
pounds. If a similar board has a width of 8
inches and a height of 5
inches, how long must it be to support 1300
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 = 13 ft
w = 4 in
h = 6 in
m = 800 lbs
Plug in these values into m = C*w*h^2/l we have:
800 = C*4*6^2/13
C = (800*13)/(4*24)
Let 'x' represent the length of the beam needed to support 1300 pounds when the board has w = 8 in and h = 5 in, that is:
1300 = C*8*5^2/x
C = (1300x)/(8*25)
Finally we need to solve the following equation:
(1300x)/(8*25) = (800*13)/(4*24)
........
click here to see the equation solved for x
........
x = 16.67 ft
The beam needs to be 16.67 feet long.