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

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AI Thread Summary
The discussion revolves around calculating how far an 800-N person can stand on a 10-m plank weighing 100 N without tipping it. The plank is supported 1 m from each end, creating a fulcrum point. Participants are attempting to set up the equilibrium equation, balancing the moments on either side of the fulcrum. The key calculations involve the weights of the person and the plank, as well as their respective distances from the fulcrum. The final goal is to determine the maximum distance from one end where the person can stand without causing the plank to tip.
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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)
 

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

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