Problema Solution
Suppose that the maximum weight that a certain type of rectangular beam can support varies inversely as its length and jointly as its width and the square of its height. Suppose also that a beam
5
inches wide,
2
inches high, and
10
feet long can support a maximum of
8
tons. What is the maximum weight that could be supported by a beam that is
6
inches wide,
2
inches high, and
24
feet long?
Answer provided by our tutors
G = C*(w*h^2/l), where C is constant
C = G*l/(w*h^2)
w = 6 in
h = 2 in
l = 10 ft
G = 8 t
C = 8*10/(6*2^2)
C = 80/24
C = 10/3
G = (10/3)*(w*h^2/l)
w = 6 in
h = 2 in
l = 24 ft
G = (10/3)*(6*2^2/24)
G = 10/3 t
G = 3.33 t
The maximum weight that could be supported by a beam that is 6 inches wide, 2 inches high, and 24 feet long is 3.33 tones approximately.