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 beam?

Question

14-08-2023
Physics

High School

We appreciate your visit to 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. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!

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 beam?

Answer :

Other Questions

The reaction of [tex]$10.0 \, \text{g} \, H_2$[/tex] with [tex]$10.0 \, \text{g}

Which of these foods is an aperitivo? A. Torta de manzana y

Complete the synthetic division problem below. [tex]2 \longdiv { 1 \quad 5

help :)))) yall amazing

If wolves did not live on Isle Royale, what main factor would

Sex: Male Height: 185 cm (6 ft 1 in) Age: 34 years

Which of the following is the correct ion for strontium (Sr)? A.

The front panel of a cereal box has an area of 97

Where is the Western Front line drawn on the Europe 1914 map?

a 12 ounce can of store-brand tomato sauce costs $ 1.37 at

Alahari275G Alahari275G · Answer 1 · 2025-05-24T16:31:35-04:00

Final answer:

The strength of a rectangular beam is directly proportional to its width and square of thickness. A 4 inches wide and 3 inches thick beam can support 504 pounds, therefore a construction manager can substitute the 4 by 3 beam in place of the 5 by 2 beam because it can support more weight.

Explanation:

The strength (S) of a rectangular beam is directly proportional to its width (w) and the square of its thickness (t) such that S = kwt^2, where k is the constant of proportionality. Given that a 5-inches wide and 2-inches thick beam supports 280 pounds, we can find k as k = S / (wt^2) which gives k = 280 / (5*2^2) = 14.

For a similar beam that's 4 inches wide and 3 inches thick, we can then find its strength S as S = kwt^2, which yields S = 14 * 4 * 3^2 = 504 pounds. Therefore, the similar beam can support 504 pounds.

Since 504 pounds is greater than 280 pounds, a construction manager could substitute the 4 by 3 beam in place of the 5 by 2. The increase in thickness has a greater impact on the strength of a rectangular beam than a decrease in width given the square relationship.

Learn more about Beam Strength here:

https://brainly.com/question/28523449

#SPJ11