💬 👋 We’re always here. Join our Discord to connect with other students 24/7, any time, night or day.Join Here!



Numerade Educator



Problem 70 Hard Difficulty

If a diver of mass $ m $ stands at the end of a diving board with length $ L $ and linear density $ p $, then the board takes on the shape of a curve $ y = f(x) $, where
$$ Ely^n = mg(L - x) + \dfrac{1}{2}pg(L - x)^2 $$
$ E $ and $ l $ are positive constants that depend on the material of the board and $ g(<0) $ is the acceleration due to gravity.
(a) Find an expression for the shape of the curve.
(b) Use $ f(L) $ to estimate the distance below the horizontal at the end of the board.


(a) $$
\begin{array}{l}{f(x)=\frac{m g}{6 E I}(L-x)^{3}+\frac{\rho g}{24 E I}(L-x)^{4}+\left(\frac{m g}{2 E I} L^{2}+\frac{\rho g}{6 E I} L^{3}\right) x} \\ {+\left(-\frac{m g}{6 E I} L^{3}-\frac{\rho g}{24 E I} L^{4}\right)}\end{array}
(b) $$
f(L)=(8 m+3 \rho L) \frac{g L^{3}}{24 E I}


You must be signed in to discuss.

Video Transcript

The problem is, if a timer off my Sam stands at his Angela for having border with laugh l onda linear dance T. Rowe, Then the board takes on the shape of a cure for why go to a fax wire. He'd have I temp swipe from prom is able to ama tree hands l minus X plus one half times. Georgie hands al minus x squared here. He and I are positive constants. That depends on the material off the board and G is acceleration. Don't shoot gravity, but a find this expression for the ship of the groove. So here from the Graff, off this function, we have y zero is equal to zero. And why fund zero is out solved. Zero Then around this expression with half he hams I y prom. Is he conscious? Negative for half tree l minus X squared. Plus it is minus one over six. Jo Gi Tam's our minus X. It is a power of three, plus some constant number C one faints. Wine wise here. Why? Prom zero is zero. So we have three one. Is he conscious? Well, half tree al square plus one over six Georgie House Cube. there. Compute! See I Why? This is the country one over six g l minus X to the power of three. Plus I won over twenty four. Georgie Al minus ax to the public. Off or us C one x us too. Face y zero. It's also Ciro. Behalf situ is equal to negative. Want over six Tree House Cube Plus won over twenty four. Georgie, How to parallel or on behalf? Why is he called to one Overeat Tams. I won't apply one over six G al minus X to the power of three. Asked one ofthe twenty four No G al minus X to the power off or us see Juan is his numbers too. Is this number this is one half V our square plus one over six Ruchi House Cube comes Axe us minus one over six omg house Cube US one hour twenty four Joji house to the power ofthe war. How to be use a half hour to estimate it's a distance between below the horizontal. I could end up with the board. It's a foul. That's why at this point off, actually goto our so f l is they want you. This isn't going to Cyril to see its equal to zero behalf. This is one over I terms well, half. I'm Chief House Cube, US one over six, Joe out to the pop off or minus one over six. I'm G House Cube minus one over twenty four. Refugee out of poverty for this is equal to one over. You passed by terms. Want over three? I'm G house too. Plus one over eight. Joji Alex Pavel for