Finding the mass of a beam by static equilibrium

[yssida]

Homework Statement

This is actually an experiment we did at class. A horizontal beam was loaded with 100 grams weight at the left end. This beam was supported (with my hands) at 30 centimeters from the left end until balance is restored by putting another weight (168 grams) on the other side, which was found out to be 6.4 centimeters from the point of support (POS) at the right side. I need to find the mass of the beam given this information.

I'll try my best to illustrate this with text

|---------X----------|-----------|

wt here POS other wt here
(100g) (168g)

Homework Equations

Torque left = Torque right; or that they will sum up to zero

T=r x F; but since weight is perpendicular then T=rF or T=rmg (since only the weight is acting on the beam); but then I need to account for the weight of the weight added and the mass of the beam itself so: T=r (mass of beam portion + mass of added obj) g

to find the mass of the beam portion, we assumed the mass was distributed evenly; hence mass beam portion = Mass beam total * r / total length

The Attempt at a Solution

I tried to Torque left=Torque right --->

r left * (mass beam left + mass added left) g = r right * (mass beam right + mass added right) g

and removed g

then I substituted the mass beam (left/right) with total mass beam * r / total length

giving me

r_left (M_total r_left/L_total + m_{added left} )=r_right (M_total r_right/L_total + m_{added right})


Is this the correct way to go about the problem? The answers I get are very far from the measured mass of the beam.

 

[Spinnor]

What is the length of the beam?

 

[yssida]

I forgot, sorry it's 98.3 cm.

 

[rl.bhat]

Weight of the bar acts at the center of the beam. Now apply

Torque left = torque right and find m.