91Ó°ÊÓ

The given data can be listed below as,

• The mass of the runner is, $50\text{kg}$.
• The velocity of the runner is, $10\text{m/s}$.
• The time taken by the runner is, $3\text{s}$.

The law of conservation of work done states that energy cannot be destroyed or created, it can only be converted into different forms.

The second law of Newton states that the force exerted is directly proportional to the product of the mass and the acceleration of a body.

According to the work-energy theorem, the work done is the same as that of the change in the kinetic energy.

(a)

The expression for the horizontal component of the force can be expressed as,

$$\begin{gathered} F=ma \\ =m\left(v/t\right) \end{gathered}$$

Here, $m$is the mass of the runner, $a$is the acceleration of the runner that is $a=\frac{v}{t}$(here, $v$is the velocity of the runner and $t$is the time taken by the runner).

For $m=50\text{kg}$, $v=10\text{m/s}$and $t=3\text{s}$.

$$\begin{gathered} F=\left(50kg\right)×\left(\frac{10m/s}{3s}\right) \\ =166.66kg.m/s^2 \\ =166.66kg.m/s^2×\frac{1N}{1kg.m{s}^2} \\ ≈167N \end{gathered}$$

Thus, the average horizontal component of the force is $167\text{N}$.

(b)

The expression for the displacement of the runner is expressed as,

$s=ut$

Here, $u$is the initial velocity of the runner’s shoes that is 0 and $t$is the time taken.

Substitute all the values in the above equation.

role="math" localid="1653903841151" $$\begin{gathered} s=0m/s×3s \\ =0m \end{gathered}$$

Thus, the displacement of the runner’s shoes is 0.

The expression for work done on the extended system can be expressed as,

$W=F·d$

Here, $F$is the force and $d$is the displacement of the runner.

For $F=167\text{N}$and $d=0$.

$$\begin{gathered} W=167N×0 \\ =0 \end{gathered}$$

Thus, the work done on the extended system is $0$.

From the law of conservation of work done, the equation of the work done on the point particle system can be expressed as,

$W_1=\frac{1}{2}m{v}^2$

Here, $W_1$is the work done on the point particle system.

For$m=50\text{kg}$and $v=10\text{m/s}$.

$$\begin{gathered} W=\frac{1}{2}×50kg×{\left(10m/s\right)}^2 \\ =2500kg.m^2/s^2 \\ =2500kg.m/s^2×\frac{1J}{1kg.m/s^2} \\ =2500J \end{gathered}$$

Thus, the work done on the point particle system by this force is $2500\text{J}$.

(c)

By the work energy theorem, the work done is same as that of the change in the kinetic energy.

As the Kinetic energy of the runner increases, the internal or the chemical energy of the runner decreases.

As the work done on the point particle system is $2500\text{J}$ so the internal energy also decreased by $2500\text{J}$.

Thus, the internal energy decreases and it reduces to $2500\text{J}$.