91Ó°ÊÓ

The given data is listed below as-

• The mass of the ball is, $m=0.8\mathrm{kg}$
• The length of a string, $l=1.6\mathrm{m}$

The Work done along a path P₁ to P₂ is given by

$\mathbf{W}\mathbf{=}{\mathbf{∫}}_{{\mathbf{P}}_{\mathbf{1}}}^{{\mathbf{P}}_{\mathbf{2}}}\stackrel{\mathbf{→}}{\mathbf{F}}\mathbf{d}\stackrel{\mathbf{→}}{\mathbf{s}}$

The force of tension is perpendicular to the direction of motion if the motion of a ball is a perfect circle. Therefore, the work done by it is 0.

The force of gravity that is directed upwards is given by

${\stackrel{→}{F}}_g=-mg\hat{z}$

The work done on the ball is given by

$W_g=-mg{∫}_{P_1}^{P_2}dz=-mg\left(z_2-z_1\right)$

When the ball went around in a full circle,$W_g=0$

The work done by Tension is zero.

Thus, the magnitude of work done on the ball by tension is zero and when the ball went around a full circle is also 0.

When the ball went from the lowest to the highest point,

$W_g=-mg\left[l-\left(-l\right)\right]$

Here, m isthe mass of the ball, g is the gravitational constant and l is the length of the spring.

For $m=0.8kg$, $l=1.6m$, and $g=9.8m{s}^{-2}$

$$\begin{gathered} W_g=-2mgl \\ =-2×0.8×9.8×1.6J \\ =-25.1J \end{gathered}$$

The work done by Tension is zero.

Thus, the magnitude of work done on the ball by tension is zero and when the ball went from the lowest to the highest point is -25.1 J.