Centre of mass and gravity problem, confused and

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Homework Help Overview

The problem involves a uniform plank and the concept of center of mass and gravity, specifically examining the conditions under which the plank remains at rest when a person stands on it. The scenario includes specific measurements for the plank's length, mass, and the distance between supports.

Discussion Character

  • Conceptual clarification, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the location of the center of mass for the plank and the system as a whole. Questions arise regarding the relationship between center of mass and center of gravity, as well as the implications of Throckmorton's position on the plank. There is also inquiry into the calculation of the center of mass using weighted averages.

Discussion Status

The discussion is ongoing, with participants exploring the definitions and calculations related to center of mass. Some guidance has been provided regarding the formula for the center of mass, but there are still questions about the reasoning behind specific values and the overall setup.

Contextual Notes

Participants are grappling with the diagram and its implications for understanding the center of gravity in relation to the system's mass distribution. There is a noted confusion about the positions used in calculations and the assumptions made regarding the center of mass.

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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:
throcky.jpg


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 ?
 
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It is the centre of mass of the system which includes all the masses.
 
paisiello2 said:
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)
 
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.
 
HallsofIvy said:
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)
 
He's taking moments about the left end.

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

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