Question

A simple pendulum of mass m and length l is initially motionless at the bottom equilibrium position, θ(0) = 0. Then, a constant horizontal force F0 = 1 2mg is applied to the particle. Find θmax for the motion which follows.

Answer 1

F₀= 12 mg θ = 85.2º

Step-by-step explanation:

When the force is applied the pendulum moves laterally, and the tension in the rope has components that reached a point balances the horizontal force. Let's apply make sure Newton

X axis

F -Tx = 0

F = Tx

Axis y

Ty -W = 0

Ty = W

Let's look for the tension components

cos θ = Ty / T

sin θ =Tx/T

Ty = T cos θ

Tx = T sin θ

Let's replace and solve the system of equations

F = T sin θ

mg = T cos θ

F / mg = tan θ

tan θ = 12 mg / mg

θ = tan -1 12

θ = 85.2º