How Far Can a Person Stand on a Plank Without It Tipping?

[gcombina]

Homework Statement

A horizontal, 10-m plank weighs 100 N. It rests on two supports that are placed 1.0 m from each end as shown in the figure. How close to one end can an 800-N person stand without causing the plank to tip?

Homework Equations

The Attempt at a Solution

This is kind of difficult to me, please help me understand this

I know the person weighs 800 and there is X distance

so I have 800N from the weight of the person plus 10 N from the weight of the plank on the right side of the fulcrum

800X + 10 N = 90 N (the weight of the rest of the plank)

 

[jedishrfu]

Isn't the formula F x Dist so that for this case (800 + 10) * X and the length on the other side would be?

 

[gcombina]

Isn't the formula F x Dist so that for this case (800 + 10) * X and the length on the other side would be?

the length of the other side would be 90 meters which equates to 90N

 

[BvU]

Not good.
On the left we have 90 N * 4.5 m (as we had in October...)
On the right we have
from the person: 800 * (1-X) if X is the distance from the end of the plank
from the plank: 10 N * 0.5 m (Haru's "the rest of the plank")

Now balance the lot and you're done.

Good luck with the exam :)