91Ó°ÊÓ

The given data can be listed below,

• The mass of the child is, $m=10\mathrm{kg}$.
• The maximum height of the triangle is, $h=10\mathrm{m}$.

If a body really moves a certain distance in the direction of the applied force, such movement is considered to constitute work. The dot product of force time distance is known as work.

When x rises during the displacement, the work done is positive is given by,

$W=\frac{1}{2}b×h$

Here, b is the base of the triangle, and h is the height of the triangle.

Substitute all the values in the above from the graph,

$$\begin{gathered} W=\frac{1}{2}\left(8\mathrm{m}\right)\left(10\mathrm{N}\right) \\ =40\left(\mathrm{N}.\mathrm{m}\right)\left(\frac{1\mathrm{J}}{1\mathrm{N}·\mathrm{m}}\right) \\ =40\mathrm{J} \end{gathered}$$

Thus, the work done by the force on the sled when it moves from$x=0$ to$x=8\mathrm{m}$ is 40 J .

When x rises during the displacement, the work done is positive is given by,

$W=\frac{1}{2}b×h$

Here, b is the base of the triangle, and h is the height of the triangle.

Substitute all the values in the above from the graph,

$$\begin{gathered} W=\frac{1}{2}\left(4\mathrm{m}\right)\left(10\mathrm{N}\right) \\ =20\left(\mathrm{N}·\mathrm{m}\right)\left(\frac{1\mathrm{J}}{1\mathrm{N}·\mathrm{m}}\right) \\ =20\mathrm{J} \end{gathered}$$

Thus, the work done by the force on the sled when it moves from$x=8\mathrm{m}$ to$x=12\mathrm{m}$ is 20 J.

When x rises during the displacement, the work done is positive is given by,

$W=\frac{1}{2}b×h$

Here, b is the base of the triangle, and h is the height of the triangle.

Substitute all the values in the above from the graph,

$$\begin{gathered} W=\frac{1}{2}\left(12\mathrm{m}\right)\left(10\mathrm{N}\right) \\ =60\left(\mathrm{N}·\mathrm{m}\right)\left(\frac{1\mathrm{J}}{1\mathrm{N}·\mathrm{m}}\right) \\ =60\mathrm{J} \end{gathered}$$

Thus, the work done by the force on the sled when it moves from $\mathrm{x}=0\mathrm{m}$to $\mathrm{x}=12\mathrm{m}$is 60 J .