91Ó°ÊÓ

The given data can be listed below as:

• The height raised by the arm is $\mathrm{h}=30\mathrm{cm}×\frac{{10}^{-2}\mathrm{m}}{1\mathrm{cm}}=30×{10}^{-2}\mathrm{m}$.
• The time taken to raise the arm is t = 1.0 s.
• The weight of the person is w = 680 N .
• The height raised by the body upward is$\mathrm{s}=15\mathrm{cm}×\frac{{10}^{-2}\mathrm{cm}}{1\mathrm{cm}}=15×{10}^{-2}\mathrm{m}$ .
• The time taken to raise the body to accelerate upward is ${\mathrm{t}}_1=0.5\mathrm{s}$.

Newton’s second law states that the reason for the acceleration of a body is due to the actions of the forces. The force exerted is directly proportional to the mass and the acceleration of an object.

The free-body diagram of the person’s body has been drawn below:

In the above diagram, the weight w is acting downwards and the force F is acting upwards. The acceleration is also acting in the upwards direction.

The equation of the acceleration of the arm is expressed as:

$s={\mathrm{ut}}_1+\frac{1}{2}{\mathrm{at}}_1^2$

Here, is the height raised by the body upward, u is the initial velocity of the arm, t is the time taken to raise the body to accelerate upward and is the acceleration of the arm.

As initially the arm was at rest, then the initial velocity of the arm is zero.

Substitute the values in the above equation.

$$\begin{gathered} 0.15\mathrm{m}=\left(0\right){\mathrm{t}}_1+\frac{1}{2}a{\left(0.5s\right)}^2 \\ 0.15m=\frac{1}{2}a\left(0.25{\mathrm{s}}^2\right) \\ 0.15m=a\left(0.125{\mathrm{s}}^2\right) \\ a=1.2\mathrm{m}/{\mathrm{s}}^2 \end{gathered}$$

The equation of the force his arms must exert is expressed as:

$$\begin{gathered} \mathrm{F}=\frac{\mathrm{W}}{\mathrm{g}}\mathrm{a}+\mathrm{W} \\ =\mathrm{W}\left(\frac{\mathrm{a}}{\mathrm{g}}+1\right) \end{gathered}$$

Here, is the force his arms must exert, is the weight of the body and is the acceleration due to gravity.

Substitute the values in the above equation.

localid="1667641792661" $$\begin{gathered} F=\left(680\mathrm{N}\right)\left(\frac{1.2\mathrm{m}/{\mathrm{s}}^2}{9.8\mathrm{m}/{\mathrm{s}}^2}+1\right) \\ =\left(680\mathrm{N}\right)\left(0.12+1\right) \\ =\left(680\mathrm{N}\right)\left(1.12\right) \\ =763.26\mathrm{N} \end{gathered}$$

Thus, the force his arms must exert is 763.26 N .