Computing magnitude and location of resultant parabolic loading

[RKOwens4]

Homework Statement

Compute the magnitude and location of the resultant of the parabolic loading shown in the figure below. The slope of the parabola is zero at the origin.

See figure: http://imageshack.us/photo/my-images/819/prob6.jpg/

Homework Equations

The Attempt at a Solution

This question is being asked in a new class but the material is from a class I took a year ago. I asked my professor for help but he's refusing to help because this is stuff we "should already know", but in the real world people don't remember every single formula that they ever went over in every class throughout their college career, and I no longer have the book for that class. It seems like this would be very, very simple to solve if I just knew the formula. I'm not asking for the final answer, but can someone help?

 

[RKOwens4]

Come on guys. 73 views and not one reply?

 

[SteamKing]

If you show your attempt at solving the problem, you might get more help.

If you don't have your old textbooks anymore, the information in them didn't vaporize. Try googling 'parabola' and see if some useful information can be obtained.

 

[RKOwens4]

If you show your attempt at solving the problem, you might get more help.

If you don't have your old textbooks anymore, the information in them didn't vaporize. Try googling 'parabola' and see if some useful information can be obtained.

I did that for half an hour before posting this thread. I also explained my attempt at a solution in my original post. Like I said in my OP, I don't expect anyone to just give me the answer (I'm above a 3.5 gpa and don't do the cramster thing like most people do... they just screw themselves when it comes to the exams). But I would appreciate a LITTLE help, like a few of the basic equations which I can use to figure the rest out on my own. Instead I get some condescending, snarky response about how the information in my books didn't just vaporize. Thanks dude, that's so helpful.

 

[SteamKing]

No, you didn't explain an attempt at a solution in your OP, you made some vague excuses about not having your textbooks, or your professor said you should already know this material, etc.

If you google 'parabola' as I suggested, check out the equation of a parabola in the Cartesian coordinates section. That will give you a start. Then you are going to need to know how to determine the equivalent load from the parabolic distribution. Then you will need to google 'area' and 'moment' in order to find the location and magnitude of the equivalent force.

Or you could order up another gallon of whine instead.

 

[davidm1732]

Start with the equation for the curve... What is it for a parabola...?
Y = ax + b ?
Y = ax^2 + bx + c ?
Y = ax^3 + bx^2 + cx + d ? ...etc

How does that relate to the loading? Imagine the load is caused by stacks of bricks... or columns of coins, etc etc... how do you determine the load of each column? The height of the column times the width (ignore density for now)... starting to look like you're going to have to integrate that equation you've chosen to represent your parabolic load curve to find the total load...that's the first part. If that's still seeming difficult, replace the parabolic curve with a simpler load case... perhaps constant load across the length, or a linearly increasing load from zero up to W at length L... to apply your solution methodology. Those problems can be solved fairly easily without integrals, and give hints towards the more complicated example.

There are several ways to find the second part...the resultant load and it's location, perhaps more intuitively than looking at the centroid of that shape function... think of a teeter totter, but with a fat kid on one end, and a skinny on on the other... where do you put the fulcrum so the bar is level? You can figure this out in a similar fashion.

 

[Pilgrimman]

Generate a formula for the parabola as a polynomial. Integrate over the bar. Apply that force at the centroid of the parabola (which can likely be found in the back of your book in a table).

 

[RKOwens4]

Or you could order up another gallon of whine instead.

You must get beat up a lot, huh? Or at least made fun of. Thus your only way of feeling "big" is trying to talk big and condescending to people who need homework help. I actually found the answer from a classmate. You're a loser, dude.