Yea I can the problem actually makes sense now :biggrin:. Thanks for helping me understand it. Now to try and prove my original method, getting docked 20 points sucks. All I'm at is that method works for all shapes that are proportional and symmetrical. Thanks for all the help Tim.
Sure, I'll just use the same tank that we have been dealing with the entire time.
Slicing the triangle into horizontal pieces, and measuring distance from the top of the tank.
We know that volume is = l*w*h
The length is constant, it is 3. The height is going to be dx.
The width is what is...
I think so, and horizontal slices would be correct. On a side note, I just saw where someone did a problem pretty much exactly like this one and for their volume they calculated the width using similar triangles and didn't keep it fixed at some value. Is this an ok method to use? It makes more...
Why do we take rectangular slices out of a triangular object? If we were to transpose a rectangular slice over the triangle wouldn't it protrude over the edges of the tank giving us a larger area than we were looking for?
Just adressed the rectangle issue with some friends since n approaches...
Ahh, ok I see what we are doing I believe. I can clearly see the height. Why is the breadth y? The breadth isn't constant, the only thing constant as far as the shape is concerned is the length of 3. And thanks for all the help Tim, whether I get to a point where I understand or not I really...
So the height and breadth are dy. Does that make sense? Since the height and base are equal and change at the same rate. Is this where I'm messing up attempting to integrate triangles.
You have a length of 3 a height of y and a breadth of y. The slice I'm picturing is the shape of a triangle. I'm thinking of our tank and just drawing a line through it horizontally with everything underneath it being the slice.
I was assuming that we were overlooking that you typed the 300gydy lol :smile: the mass is 3000gydy. Assuming that the bottom of the triangle is y, the height would be y+dy, so that makes sense.Scratch the trapezoid thing I said earlier, needed to draw a picture which says that is obviously...
I'm not saying you made a mistake, you have a method that you can support with calculus and justify what you have done, and it works for this problem and others. I feel like the volume should be 3 times the area of a trapezoid with height y, I'm not sure what your bases would be. That would give...
Why is the volume 3000gydy? I just don't see the units working. I see a F/m3 *m*m. (Sorry for not putting the dy's, I know they go there, I'm just used to people assuming that it was there. It was never stressed those were important to write, but I guess I can see where I should have.)
Sure thing, my teacher does it like so.
Mass=density*volume
So 1000*3*y
Force=mg
so 1000*3*y*g
And Work is force times a distance
The distance is going to be 1-y
this gives us 1000*3*g*∫y*(1-y) with the integral being from 0 to 1
This yields us 3000g*((1/2)y2-(1/3)y3) evaluated at 0 to...
He is correct, he asked me to support what I did, and I can't in a way that he and I understand. I can prove it works for problems of the same type, just not visually enough I guess. If I can show him the distance part he will give me credit, as that is his main discrepancy. My weekend is going...
None at all. That was my thought process, I follow units in problems I don't have a full grasp on, which works in many cases as the unit leads you to the answer. It works in this problem and all the other work problems for the triangle in which the base and the height are equal and changing at...
The integral is l*1000*g*∫(1/2)*b*h
The way I did this problem is I followed the units. I know that 1000(the mass density)*g will give me N/m3. Next I thought ok, the integral of an area will give me a cubic function. So I integrated the area of a triangle, or (1/2)*b*h. I know that for this...
Homework Statement
A tank of water is 3m long and has a triangular cross section of height 1m and width at the top of 1m. How much work is done pumping the water to the top of the tank? The density of water is 1000kg/m3 and the gravitational constant g has value g m/s2
Homework Equations...