Question

The bob of a simple pendulum of length $1m$ has mass of $100g$ and has a speed of $1.4m/s$ when the string makes an angle of $0.2rad$ with the vertical. Find the tension at this instant. You can use $cos\theta =1-{\theta }^2/2$ and $sin\theta =\theta$ for small $\theta$.

Answer 1

The free body diagram for the given scenario is shown in the figure.

Centripetal force acting is:

$F_c=T-mg\cos \theta$

$T\approx mg\theta +\frac{m{v}^2}{R}$

$=.1\times 10\times (1-{.2}^2/2)+\frac{.1\times {1.4}^2}{1}$

$=1.176N$