Can a 66kg Person Sit on a 24kg Table Without Tipping?

[ajcoelho]

This is a very well known physics problem and i already know how to solve it.

How close to the edge of a 24kg table can a 66kg person sit without tipping it over?

I think everybody can see the table and what's happening in there.

MY QUESTION IS:

Why don't we use the normal reaction due to the farther suportting?? I mean, when we calculate total torque about one supporting, we still have the other support in which there's a reaction force ating. And i think this force is as legitimate as the gravity forces of the table and person...

I would be really glad with any answer trying to explain why is this approximation made or if I'm completely wrong in my reasoning!

Take care!

 

[tiny-tim]

hi ajcoelho!

Why don't we use the normal reaction due to the farther suportting??

because it's zero!

so long as the total reaction force from the floor (the resultant of the reaction forces from the four legs) goes through the base of the table (the rectangle with the legs at the corners), the table will not tip

the table will only start to tip when the resultant reaction force goes through the edge of the base

when that happens, the individual reaction forces through the farther legs will be zero

 

[ajcoelho]

the table will only start to tip when the resultant reaction force goes through the edge of the base

when you say edge of the base you're referring to the supporting that has become a "pivot"?

 

[tiny-tim]

yes, when the reaction force reaches the edge, the tip will start about that edge as pivot

 

[HalfLostAndSearching]

I would like to address your question about using the normal reaction force from the farther supporting as a part of the calculation for the tipping point of the table and person. The reason why this is not included in the calculation is because it does not contribute to the torque on the system.

When we calculate the tipping point of the table and person, we are determining the point at which the torque from the person's weight is equal to the torque from the table's weight. The normal reaction force from the farther supporting does not create any torque because it acts perpendicular to the surface of the table. Therefore, it does not play a role in determining the tipping point.

Additionally, when we consider the stability of a system, we only need to consider the forces and torques that are acting on the system. The normal reaction force from the farther supporting is an external force that is not acting on the system itself, but rather on the supporting structure. Therefore, it is not relevant in determining the tipping point of the table and person.

I hope this explanation helps to clarify why the normal reaction force from the farther supporting is not included in the calculation for the tipping point. If you have any further questions, please do not hesitate to ask.