Question

Three masses hang about a meter stick whose fulcrum is at 20cm. A mass of m1=40.0 kg hangs at the 70.0 cm mark, m2= 30.0 kg hangs at the 30.0 cm mark and mass m3 = 20kg is located at the 50 cm mark. The mass of a metal washer, mw is hanging from the 15cm mark.

a) Find the mass of the metal washer, mw needed to obtain static equilibrium.
b) If the mass in part A is not realistic, then draw a diagram that will render a reasonable value.
c) Complete the problem again when the fulcrum is located at the 50 cm mark.
d) Repeat the problem above when the pivot point(axis of rotation) is located at the 60 cm mark of the meter stick.

Answer 1

A) Find the mass of the metal washer, mw needed to obtain static equilibrium.

To obtain static equilibrium, the sum of the torques on the meter stick must be zero. This can be expressed mathematically as:

Στ = 0

Where Στ is the sum of the torques and is calculated by:

Στ = r1F1 + r2F2 + r3F3 + rwmw

Where r is the distance of the mass from the fulcrum and F is the force due to gravity acting.