Help pleeeease :3

Question

Help pleeeease :3

itz_sid · Answer

Kay, here is the last question to my homework. I need help understanding it :/

irishboy123 · Answer

for a they even gave you the units!!

loser66 · Answer

|dw:1476060141630:dw|

loser66 · Answer

The rope weighs is 0.02 lbs / foot.

loser66 · Answer

Hence $W\int_0^{30} 0.02x dx$

loser66 · Answer

dat sit!! :) 
Or I underestimate the problem??

loser66 · Answer

On the computer, you need type $"0.02*x_i^* \triangle x$

itz_sid · Answer

wouldnt gravity play a role in it?

loser66 · Answer

Is it not that gravity is included on calculating mass?

loser66 · Answer

I don't know physics!! :)

irishboy123 · Answer

you're using weird American units

but indeed, g should be in there

irishboy123 · Answer

If you're still wondering about the units and where gravity comes in, look at the mini-integration they first suggest on that page you attached:

$W_1 = \int \dfrac{3}{5} x ~ dx  $


....where the $\dfrac{3}{5} $ is the $ 0.6 \dfrac{lb}{ft}$ linear density of the rope

So the units of $W_1$, shown in red below, are

$\int \dfrac{3}{5} \color{red}{(\dfrac{lb}{ft})} x \color{red}{(ft)} ~ dx \color{red}{( ft )}  = lb ~ ft  \qquad \triangle$

$W_1$ is supposed to be a work calculation, which (put crudely) is the same as energy, and should have units that follow the idea that 

$W = F \cdot x = m \cdot \color{blue}{a} \cdot x $

....which has units

$lb \cdot \color{blue}{\dfrac{ft}{s^2}} \cdot ft = \dfrac{lb ~ {ft}^2}{s^2}$

You haven't got that because the middle *blue* bit is missing; but you would if you multiplied what you have with the units of acceleration (which are the units of gravity), ie: 

$\dfrac{ft}{s^2}$

So whatever you get from this odd way of doing things, well to make the numbers actually useful, you need to multiply by a factor of g.  which i think you know already.

irishboy123 · Answer

and you don't actually need calculus here, you can just model it as a point mass.

itz_sid · Answer

kay, so i got this far, but dont know what to do next. And i need help with part a still.

itz_sid · Answer

@zepdrix

itz_sid · Answer

I'm trying to understand it, but i honestly just dont get it.

itz_sid · Answer

Lmao. never mind. I got it