The strength S of a rectangular beam varies jointly as its width w and the square of its thickness t. If a wood beam 3 inches wide and 5 inches thick supports 300 pounds, how much can a similar beam 3 inches wide and 8 inches thick support?
S=? pounds
A.l=kbd2/S
S(w,t) = kwt^2
Find k:
300 = k*3*25
k=4
So, S(w,t)=4wt^2
S(3,8) = 4*3*64 = 768
The strength of a rectangular beam varies jointly with its width and the square of its depth. If the strength of a beam 2 inches wide by 10 inches deep is 1200 pounds per square inch, what is the strength of a beam 8 inches wide and 12 inches deep?
btrug
Ano ang pamilya
To determine the strength (S) of the second beam, we can use the joint variation equation:
S = k * w * t^2
where S is the strength, w is the width, t is the thickness, and k is the constant of variation.
We are given the first beam's dimensions and strength:
w₁ = 3 inches
t₁ = 5 inches
S₁ = 300 pounds
We can now solve for the constant of variation (k) by substituting the given values into the equation:
300 = k * 3 * 5^2
300 = k * 3 * 25
300 = 75k
To find the value of k, we divide both sides of the equation by 75:
k = 300 / 75
k = 4
Now that we have the value of k, we can substitute it into the equation to find the strength (S₂) of the second beam:
w₂ = 3 inches
t₂ = 8 inches
S₂ = 4 * 3 * 8^2
S₂ = 4 * 3 * 64
S₂ = 768 pounds
Therefore, a similar beam with a width of 3 inches and a thickness of 8 inches can support 768 pounds.