Given:
The mass is m = 0.25 g
The height of point 3 is h = 1.9 m
The pendulum is at rest at point 3, so its speed will be zero at this point.
The height of point 2 is h' = 1.6 m
To find the speed at point 2.
Explanation:
According to the conservation of energy, the total energy at point 3 is equal to the total energy at point 2.
Also,
[tex]\begin{gathered} Total\text{ energy =P.E. +K.E.} \\ E=\text{ mgh+}\frac{1}{2}mv^2 \end{gathered}[/tex]
Here, g = 9.8 m/s^2 is the acceleration due to gravity.
Total energy at point 3 is
[tex]\begin{gathered} E=0.25\times9.8\times1.9+\frac{1}{2}\times0.25\times0^2 \\ =4.655\text{ J} \end{gathered}[/tex]
The speed at point 2 can be calculated as
[tex]\begin{gathered} E=mgh^{\prime}\text{ +}\frac{1}{2}mv^{\prime2} \\ E-mgh^{\prime}=\frac{1}{2}mv^{\prime2} \\ 4.655-(0.25\times9.8\times1.6)=\frac{1}{2}\times0.25\times v^{\prime2} \\ v^{\prime}=\sqrt{\frac{2\times0.735}{0.25}} \\ =2.42\text{ m/s} \end{gathered}[/tex]
Thus, the speed of the pendulum at point 2 is 2.42 m/s
