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riadik2000 [5.3K]
4 years ago
10

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.
Physics
1 answer:
Dennis_Churaev [7]4 years ago
6 0

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

U_{\theta} = mg\Delta h = mg(L - Lcos\theta) = mgL(1 - cos\theta)

where g is the gravitational constant

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