Calculating the Mass of a Uniform Scaffold Pole with Attached Brackets

[Firepanda]

A uniform scaffold pole of length 5m has brackets bolted to it as shown in the diagram below. The mass of each bracket is 1kg.

http://img502.imageshack.us/my.php?image=mechanicseb9.png

The centre of mass is 2.44m from the left hand end. What is the mass of the pole?My attempt:

I tried using the equation

moment of whole mass at centre of mass = sum of moments of individual masses

where

x = mass of pole

whole mass = (8 + x)

moment of whole mass = 2.44

sum of moments = 17

so:

(8+x)*2.44 = 17

yet this is obviously wrong. The answer should be somewhere around 42kg.

Thx for any help :)

 

[mjsd]

this is a simple Center of Mass problem I believe where you have to "reverse engineer" and find the mass of pole. So, think about how you would find the Center of Mass of the system IF you have known the mass of the pole (which I presume has uniform mass distribution).

hint: where is the center of mass of the pole alone if it has uniform mass distribution?
when you have several point masses how do you find the center of mass of this system of point masses?

 

[Firepanda]

well if i knew the mass of the pole i could put 42 in as x, which gives me a sum of the moments of the individual masses as 122. So did i get the sum of the moments wrong?

 

[Firepanda]

maybe if i think about it like this:

taking x to be the centre of mass and 42x to be the sum of the moment at the centre of mass of the pole

50x = 17 + 42x

x = 2.125

 

[Firepanda]

reversing this like you say:

taking x as mass of the pole again (and cntre of mass to be 2.44)

(8 + x)*2.44 = 17 + 2.44x

but this is obviously wrong again

 

[mjsd]

i am really lost at why are you doing things like this...
there are basically 9 "point masses" distributed on a straight line! and your task is to find the center of mass of this system.

firstly, work out the location of the center of mass of the pole which is nothing but the mid-way point if mass distribution is uniform,

then consider the baskets as point masses so you have 9 points on a line.
next select a reference frame (ie. a coordinate system) so that you have an origin to relate distances...look at your formula for working out the center of mass of a system of particles... and then solve the equation for mass of pole...

am I missing something? this seems rather "easy"

you been saying "moments", moments about what? it is meaningless unless you have an origin or axes... I know where you get the 17 from.. but you should really be more precise on your language

 

[mjsd]

and yes.. the answer is exactly 42Kg

 

[Firepanda]

could u show me how u did it please :) its from an excersise which uses moments in every question with the one forumla i have, it works for every question for me apart from this one. mayb ur using a diferent forumla which id love to know about :)

 

[mjsd]

ok.. now I can see where you 've gone wrong... you made just one error.. the position of the center of mass the pole alone is not 2.44 from the left.. it should be at mid-point of the pole.

 

[Firepanda]

can u show me ur exact calculation? u don't have to explain it, ill see what i did wrong myself:)

 

[mjsd]

reversing this like you say:

taking x as mass of the pole again (and cntre of mass to be 2.44)

(8 + x)*2.44 = 17 + 2.44x

but this is obviously wrong again

this is very close... except on RHS it is not 2.44 but the distance from left to mid-point of pole (where the center of mass of the pole lies)...which is just...
5/2 :)

 

[Firepanda]

thankyou!