The bob of a simple pendulum of length 1 m has mass 100 g and a speed of $1.4 \mathrm{~m} / \mathrm{

Question

The bob of a simple pendulum of length 1 m has mass 100 g and a speed of $1.4 \mathrm{~m} / \mathrm{s}$ at the lowest point in its path. Find the tension in the string at this instant.

Professor PC Thomas Classes · Answer

At the lowest point of the pendulum's path, the net upward force provides the necessary centripetal force. The equation of motion is: 
$ T-m g=\frac{m v^2}{L} $
Rearranging for Tension ( $T$ ): 
$ T=m\left(g+\frac{v^2}{L}ight) $
Given: $m=100 \mathrm{~g}=0.1 \mathrm{~kg}, v=1.4 \mathrm{~m} / \mathrm{s}, L=1 \mathrm{~m}, g=9.8 \mathrm{~m} / \mathrm{s}^2$.
$ \begin{aligned} & T=0.1 	imes\left(9.8+\frac{(1.4)^2}{1}ight) \ & T=0.1 	imes(9.8+1.96) \ & T=0.1 	imes 11.76=1.176 \mathrm{~N} \approx 1.18 \mathrm{~N} \end{aligned} $