Centre of mass and gravity problem, confused and

[TheRedDevil18]

Homework Statement

A uniform plank of length l = 6m and mass M= 90kg rests
on sawhorses separated by D = 1.5m and equidistant from the
center of the plank. Cousin Throckmorton wants to stand on the
right-hand end of the plank. If the plank is to remain at rest, how
massive can Throckmorton be?

Diagram:

Homework Equations

The Attempt at a Solution

I am confused at the diagram. Why is the centre of gravity not at the centre of mass of the plank which should be in the middle ?

 

[paisiello2]

It is the centre of mass of the system which includes all the masses.

 

[TheRedDevil18]

It is the centre of mass of the system which includes all the masses.

Okay, then how do we find it ?, or what is the explanation that says it should be there ? (referring to the cg in the image)

 

[HallsofIvy]

The center of mass of the plank is at the middle of the plank. Taking x to be the distance from the left end of the plank, that would be x= 3.0. Throckmorton's center of mass is where he is standing at x= 6.0. The center of mass of the system is a weighted average, weighted by their masses: (90*3+ M*6)/(M+ 90) where M is Throckmorton's weight.

 

[TheRedDevil18]

The center of mass of the plank is at the middle of the plank. Taking x to be the distance from the left end of the plank, that would be x= 3.0. Throckmorton's center of mass is where he is standing at x= 6.0. The center of mass of the system is a weighted average, weighted by their masses: (90*3+ M*6)/(M+ 90) where M is Throckmorton's weight.

Why is it m*6 and not m*3 ? and how do you know where the centre of gravity is ?( cg in the diagram)

 

[paisiello2]

He's taking moments about the left end.

He's giving you the formula for the location of CG