# Center of gravity of a plank

## Homework Statement

A uniform plank of length 4.6 m and weight 210 N rests horizontally on two supports, with 1.1 m of the plank hanging over the right support. To what distance x can a person who weighs 448 N walk on the overhanging part of the plank before it just begins to tip?

## Homework Equations

W1(x1)=W2(x2) = Xcm
W1+W2

## The Attempt at a Solution

210(3.5) + 658(1.1)

210 + 448

Xcm=1.87m

Not even sure if this is right, and I'm stuck after this. The way I understand it, once the center of gravity passes the second support, the plank will start to tip. But I don't know how to figure out how to calculate how far the person can walk before the center of gravity gets to that point.

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PhanthomJay
Homework Helper
Gold Member

## Homework Statement

A uniform plank of length 4.6 m and weight 210 N rests horizontally on two supports, with 1.1 m of the plank hanging over the right support. To what distance x can a person who weighs 448 N walk on the overhanging part of the plank before it just begins to tip?

## Homework Equations

W1(x1)=W2(x2) = Xcm
W1+W2

## The Attempt at a Solution

210(3.5) + 658(1.1)

210 + 448

Xcm=1.87m

Not even sure if this is right, and I'm stuck after this. The way I understand it, once the center of gravity passes the second support, the plank will start to tip. But I don't know how to figure out how to calculate how far the person can walk before the center of gravity gets to that point.
your moment calculations are way off. Hint: The plank will start to tip when the reaction at the left support goes to zero...does that help?

I don't understand...

W1(x1)=W2(x2) = Xcg
W1+W2

Is this the wrong equation?

Last edited:
PhanthomJay
Homework Helper
Gold Member
I don't understand...

W1(x1)=W2(x2) = Xcg
W1+W2

Is this the wrong equation?
I don't know what you're trying to do with this equation which has some arbitrary numbers in it. When the left support reaction goes to zero, then the moment about the right support, from the cg of the planks weight, must balance the moment about the right support from the person's weight. Equate the moments and solve for the distance from the person to the right support. As he walks beyond that point, the plank tips because the left support cannot withstand an upward load (assuming its not bolted down, in which case she'd never tip).

ok i'm still completely lost...could you maybe baby step me through this?

PhanthomJay