Question

A pendulum is swinging in a circular path at angle θ and string length L. What is the tension in the string? Use m, g, and θ. Your answer should have m, g, θ, and a trig function. Your answer will be T=. What is the centripetal acceleration? Your answer will have g, θ, and 1 or 2 trig functions.

Your answer will be ?​

Answer 1

1) T sin θ = m v^2 / R tension in string directed towards center

2) T cos θ = m g tension in string in vertical direction

sin θ / cos θ = tan θ = v^2 / (R g) dividing equations

3) θ = tan^-1 (v^2 / (R g))

From 2) T = m * g / cos θ where θ is given by 3)

(T depends on m)

v^2 / R = T sin θ / m centripetal acceleration using 1)

θ is given by 3)