Split the rod into three equal parts $($each having length $).$ Assume that each of the three pieces is short enough so that its mass density can be considered constant, equal an $$average value$$ the mass density at the center the piece. First compute the y$-$coordinates of the three centers and then using the mass density formula calculate the mass of each rod segment. Now the rod can be replaced with three point like masses located at the three segment centers.$$ Find the gravitational potential energy of each mass and then compute the $($approximate$)$ Gravitational Potential Energy of the Rod by adding the three contributions. Use$$g$=10$ m$/$s$2$when entering your answers.

In Part $3$ you will answer the following questions.

What is the length of each of three rod two segments?$$

What is the y coordinate of the center of the first from bottom rod segment?$$

What is the value of the mass density at the center of the first from bottom rod segment?$$

What is the approximate value of the mass of the first from bottom rod segment?

What is the approximate value of the Gravitational Potential Energy of the first from bottom Rod Segment?$$

What is the y coordinate of the center of the second from bottom rod segment?

What is the value of the mass density at the center of the second from bottom rod segment?$$

What is the approximate value of the mass of the second from bottom rod segment?$$

What is the approximate value of the Gravitational Potential Energy of the second from bottom Rod Segment?

What is the y coordinate of the center of the third from bottom rod segment?

What is the value of the mass density at the center of the third from bottom rod segment?$$

What is the approximate value of the mass of the third from bottom rod segment?$$

What is the approximate value of the Gravitational Potential Energy of the third from bottom Rod Segment?

What is the $($approximate$)$ Gravitational Potential Energy of the rod?