# Homework Help: Centre of mass and gravity problem, confused and need help

1. May 24, 2014

### TheRedDevil18

1. The problem statement, all variables and given/known data

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:

2. Relevant equations

3. 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 ?

2. May 24, 2014

### paisiello2

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

3. May 24, 2014

### TheRedDevil18

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)

4. May 24, 2014

### 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.

5. May 24, 2014

### TheRedDevil18

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

6. May 25, 2014

### paisiello2

He's taking moments about the left end.

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