Problema Solution
The strength S of a rectangular beam varies jointly as its width w and the square of its thickness t. If a beam 5 inches wide and 2 inches thick supports 280 pounds. How much can a similar beam 4 inches wide and 3 inches thick support? Could a construction manager substitute the 4 by 3 beam in place of the 5 by 2?
Answer provided by our tutors
S(w,t) = kwt^2, where k is constant
w = 5 in
t = 2 in
S = 280 lbs
We use this info to find k:
k*5*2^2 = 280
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click here to see the equation solved for k
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k = 14
The equation for the strength is:
S(w,t) = 14*wt^2
For w = 4 in and t = 3 in we have:
S = 14*4*2^2
S = 224 lbs
4 inches wide and 3 inches thick bean can support 225 pounds.
If the construction manager substitutes the 4 by 3 beam in place of the 5 by 2 the strength will be less 225 < 280 so it is not a good idea to decrease the strength.