A straight rod of negligible mass is mounted on a frictionless pivot as in Figure. Masses m₁ and m₂ are suspended at distances l₁ and l₂.?

(a) Write an expression for the gravitational potential energy of the masses as a function of the angle ? made by the rod and the horizontal.?

(b) For what angle ? is the potential energy a minimum? Is the statement "systems tend to move toward a configuration of minimum potential energy" consistent with your result??

(c) Show that if m₁l₁ = m₂l₂, the potential energy is the same for all values of ?. (When this holds, the system will balance at any angle ?. This result is known as Archimedes' law of the lever.)

Transcribed Image Text:

4 Tul 4 To m₂