What is the weight of a meter stick, balanced at 39.2 cm and a mass of 49g hanging at 11 cm?

Question

A meter stick is found to balance at the 49.7 cm mark when placed on a fulcrum. When a 49.0 gram mass is attached at the 11.0 cm mark, the fulcrum must be moved to the 39.2 cm mark for balance. What is the mass of the meter stick?

Answer 1

The way to solve this is to sum the torques about the fulcrum.
Lets call the mass of the stick m

The center of mass of the stick is located at 49.7 cm from the left end.

When the 49.0 g mass is added let's evaluate the torques.
Set the sign convention that clockwise torque is positive and counter clockwise is negative. Torque = F*d
I will leave out gravity since it will divide out anyway

the distance from 39.2 to 11 where the 49.0 g mass hangs is
28.2 cm to the left
The distance from 39.2 to 49.7 where the center of mass of the stick is located is 10.5 to the right
Therefore
m*10.5-49.0*28.2=0
m=49.0*28.2/10.5

m=131.6 grams

j