A rectangular beam which is supported at its two ends and leaded in the middle with weight $w$ sags by an amount $\delta$ such that $\delta = \frac{wl^{3}}{4Yd^{3}},\$where $l,d$ and $Y$ represent length, depth and elasticity respectively. Guess the unknown factor using dimensional considerations

Question

Dr. Abubacker · Accepted Answer

[?] = $\frac{\lbrack Sl^{3}\rbrack}{\lbrack 4yd^{3}\delta\rbrack} = \frac{\left\lbrack MLT^{- 2} \right\rbrack\left\lbrack L^{3} \right\rbrack\lbrack L^{2}\rbrack}{\left\lbrack MLT^{- 2} \right\rbrack\left\lbrack L^{3} \right\rbrack\lbrack L\rbrack} = \lbrack L\rbrack$

Q. A rectangular beam which is supported at its two ends and leaded in the middle with weight $w$ sags by an amount $\delta$ such that $\delta = \frac{wl^{3}}{4Yd^{3}},\$where $l,d$ and $Y$ represent length, depth and elasticity respectively. Guess the unknown factor using dimensional considerations

Explanation

Reviewed by Dr. Abubacker

Want more practice?