Respuesta :
Answer:
a) [tex]83.3\ lb/in^2[/tex]
b) [tex]12000\ lb/ft^2[/tex]
Step-by-step explanation:
Given : A weight of 18,000 lb is supported on a rectangular base plate that is 9 in. wide and 2 ft long. The base plate rests on a concrete slab.
To find : Determine the stress that the base plate exerts on the concrete slab. Express your answer in units of (a) lb/in². and (b) lb/ft².
Solution :
a) A rectangular base plate that is 9 in. wide and 2 ft long.
Converting ft into inches,
1 feet = 12 inch
2 feet = 2×12= 24 inch
The area of the rectangular base is [tex]A=l\times b[/tex]
[tex]A_1=24\times 9[/tex]
[tex]A_1=216\ in^2[/tex]
The weight is W=18,000 lb.
The stress that the base plate exerts on the concrete slab is given by,
[tex]S=\frac{W}{A_1}[/tex]
[tex]S=\frac{18000\ lb}{216\ in^2}[/tex]
[tex]S=83.3\ lb/in^2[/tex]
b) A rectangular base plate that is 9 in. wide and 2 ft long.
Converting inches into ft,
1 inch = [tex]\frac{1}{12}\ ft[/tex]
9 feet = [tex]\frac{9}{12}=0.75\ ft[/tex]
The area of the rectangular base is [tex]A=l\times b[/tex]
[tex]A_2=2\times 0.75[/tex]
[tex]A_2=1.5\ ft^2[/tex]
The weight is W=18,000 lb.
The stress that the base plate exerts on the concrete slab is given by,
[tex]S=\frac{W}{A_2}[/tex]
[tex]S=\frac{18000\ lb}{1.5\ ft^2}[/tex]
[tex]S=12000\ lb/ft^2[/tex]
