Question

If a simple pendulum of length l has maximum angular displacement θ, then the maximum K.E. of bob of mass m is(a) $\frac{1}{2}\frac{ml}{g}$(b) $\frac{mg}{2l}$(c) mgl(1- cos θ) (d) mgl sin θ/2

Answer 1

answers · Physics

Best Answer

Use L for length to avoid confusion with (eye) or (one)

If θ is measured from vertical, then at the point where the mass has no velocity, it will have maximum potential energy.

The maximum kinetic energy found when the mass is at the lowest point (angle of 0) will equal the mass gravity potential energy at angle of θ

The height the mass has risen is found via geometry

At the lowest point, the mass is a distance L below the pivot center

At angle θ, the mass is a distance of Lcosθ below the pivot center

The change in height h is the difference between these

h = L - Lcosθ

h = L(1-cosθ)

KE = PE = mgh

KE = mgL(1 - cosθ)