A pendulum consists of a massless stiff rod of length L hanging from a nearly frictionless axle, with a mass m at the end of the rod. Calculate the gravitational potential energy as a function of the angle, θ, measured from the vertical. Set U = 0 at the location of the mass when the pendulum is hanging straight down.
Answer:
mgL(1 – cosθ)
Explanation:
At angle θ, the vertical distance from the mass m to the pivotal axle is Lcosθ. While at U=0, this distance is L. Due to the mass is hanging straight down. Therefore the vertical distance from this lowest point to point at angle θ is
L – Lcosθ
The change in potential energy would be this height difference times mg
[tex]U_{\theta} = mg\Delta h = mg(L – Lcos\theta) = mgL(1 – cos\theta)[/tex]
where g is the gravitational constant