Question

The mass is 0.25 kg and the point 3 is 1.9 m and point 2 is 1.6 m

Answer 1

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.

Step-by-step explanation:

According to the conservation of energy, the total energy at point 3 is equal to the total energy at point 2.

Also,

`\begin{gathered} Total\text{ energy =P.E. +K.E.} \\ E=\text{ mgh+}(1)/(2)mv^2 \end{gathered}`

Here, g = 9.8 m/s^2 is the acceleration due to gravity.

Total energy at point 3 is

`\begin{gathered} E=0.25*9.8*1.9+(1)/(2)*0.25*0^2 \\ =4.655\text{ J} \end{gathered}`

The speed at point 2 can be calculated as

`\begin{gathered} E=mgh^(\prime)\text{ +}(1)/(2)mv^(\prime2) \\ E-mgh^(\prime)=(1)/(2)mv^(\prime2) \\ 4.655-(0.25*9.8*1.6)=(1)/(2)*0.25* v^(\prime2) \\ v^(\prime)=\sqrt{(2*0.735)/(0.25)} \\ =2.42\text{ m/s} \end{gathered}`

Thus, the speed of the pendulum at point 2 is 2.42 m/s