how do i set this up?

Question

A meter stick is balanced at the 25 cm mark when a 265 g mass is placed at the 0-cm mark. What is the mass of the meter stick in grams?

Answer 1

Set up and solve equilibrium of moments about the balance point. Put the weight of the 265 g mass at 0 cm, and put the weight of the stick mass at the center of mass of the stick, which is at the midpoint of the stick, i.e. at 50 cm from 0, which happens to be 25 cm from the balance point (the stick is 100 cm long).

m = 265 g

x₁ = distance from location of 265 g mass to the balance point = 25 cm

M = unknown mass of meter stick = ?

x₂ = distance from balance point to center of mass of meter stick = 25 cm (i.e. 50 cm from the ends of the stick)

g = acceleration of gravity

Equilibrium of moments:

mgx₁ = Mgx₂

mx₁ = Mx₂

M = (x₁/x₂)m

Plug in the numbers and finish from here.