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
`a_(c)`=.

Answer 1

T = mg / cos θ

ac = g tan θ

Step-by-step explanation:

Draw a free body diagram. There are two forces acting on the pendulum bob. A tension force T acting θ from the vertical, and gravity pulling down.

Sum the forces in the y direction:

∑F = ma

T cos θ − mg = 0

T = mg / cos θ

Sum the forces in the centripetal direction (towards the center).

∑F = ma

T sin θ = m ac

ac = T sin θ / m

Substitute for tension T:

ac = (mg / cos θ) sin θ / m

ac = (mg / m) (sin θ / cos θ)

ac = g tan θ