Plank and torque, problem with finding center mass

[paul11]

Homework Statement

A uniform plank of length 5.0 m and weight 212 N rests horizontally on two supports, with d = 1.41 m of the plank hanging over the right support. To what distance, x, can a person who weighs 433 N walk on the overhanging part of the plank before it just begins to tip?

Homework Equations

Tnet = 0
T = r * F

The Attempt at a Solution

I already found the answer, but there's something that bugs me.

Torque of plank = Torque of person
212N * 1.09m = 433N * distance

The right support is the fulcrum point.

What I don't understand is why the plank's weight acts on is 1.09m. I know the idea to get the midpoint from the two supports then subtract by the plank that is hanging over the right support, 5.00m / 2 - 1.41m = 1.09m, but I don't understand why this is the case.

This is what I initially did, 5.00m + 1.41m = 6.41m, then I divided this value by 2 to get 3.205m, and this is the center point of the plank from either end point. This point will be 1.795m from the right support, and I used this to calculate the torque of the plank. Could someone enlighten me why this was wrong? And why the correct way is .. correct?

 

[PhanthomJay]

The beam is 5.0 m in overall length. The distance between supports is 3.59 m. You have misinterpreted the beam as being 6.41 m long and the distance between supports as being 5 m. This is not what is given.

 

[paul11]

ah thank you, I need to read it more clearly.

 

[technician]

It is a good idea to draw a diagram showing all the forces acting.
The plank is uniform so the weight of 212N is acting at the centre of the plank (2.5m from each end). This should help to see the distancesa from forces and pivots.

 

[asteriatic]

I can understand your confusion about the distance at which the plank's weight acts. This is because the center of mass, or the point at which the weight of an object can be considered to act, is not always at the geometric center of the object. In the case of the plank, the weight is distributed evenly along its length, but the overhanging portion has a greater distance from the right support, causing the center of mass to shift towards the left support. This is why the correct distance to use in your calculation is 1.09m, as it represents the distance from the right support to the center of mass of the plank. This concept is important in understanding the stability and balance of objects, and it is crucial to consider the location of the center of mass when analyzing forces and torques. I hope this explanation helps to clarify the issue for you.