Question

A simple pendulum of mass m is suspended from a string of length l. What constant horizontal force must be applied on it so that string makes a maximum angle 60 from vertical

Answer 1

Answer on Question #49352, Physics, Mechanics - Kinematics - Dynamics

A simple pendulum of mass $m$ is suspended from a string of length $l$ . What constant horizontal force must be applied on it so that string makes a maximum angle 60 from vertical

Solution

The force on a mass in projection:

1. OX:

$$F = T \sin \theta$$

1. OY:

$$m g = T \cos \theta$$ $$\frac {F}{m g} = \tan \theta \rightarrow F = m g \tan \theta$$

Answer: $F = mg \tan \theta$

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