Answer:
Safe Load is 127 lb.
Step-by-step explanation:
Given:
Load (L) = 1090 lb.
width(w) = 6 in.
depth (d) = 9 in.
length (l) = 12 ft.
Since all other units are in inches and unit of length is in feet, So we will convert foot into inches we get;
1 feet = 12 inches
12 feet = [tex]12\times12 =144 in.[/tex]
Hence length(l)= 144 in.
Now also Given
Load varies directly with width and square of depth and inversely with length.
Hence we can say that;
L∝ [tex]\frac{wd^2}{l}[/tex]
Hence [tex]L=\frac{kwd^2}{l}[/tex] where k is constant.
Now Substituting the given values we will find the value of k we get;
[tex]1090=\frac{k\times6\times9^2}{144}\\\\1090=\frac{k\times6\times81}{144}\\\\1090\times144= 486k\\\\k=\frac{1090\times144}{486}\approx 322.96[/tex]
Also Given:
width(w) = 5 in.
depth(d) = 4 in.
length(l) = 17 ft.
1 ft. = 12 in.
17 ft = [tex]12 \times 17 = 204\ in.[/tex]
Hence length(l) = 204 in.
k = 322.96
We need to find the load beam(L);
[tex]L=\frac{kwd^2}{l}[/tex]
Substituting new values we get;
[tex]L = \frac{322.96\times 5\times 4^2}{204} = \frac{322.96\times 5\times 16}{204} = 126.65\ lb[/tex]
Rounding the load in nearest pound we get;
Load beam(L) = 127 lb
Hence Safe Load is 127 lb.
