Finding the weight of the planck

[adjacent]

Homework Statement

The information is on the attachment
the plank is uniform meaning the mass of the plank is uniformly spread so the center of gravity is in the mid point of the plank.The plank is in equilibrium.Find the weight of the plank,Let the weight be w.

Homework Equations

torque-f1d1=f2d2

The Attempt at a Solution

15*0.5=w*0.3
so weight is 25N

Question
But my question is the center of gravity is taken by considering the torques on the sides of it to cancel.But one piece of the plank is on the other side of the pivot.so the force on the right side cannot be taken as the center of the gravity because on piece of the plank belongs to the left side.But in my textbook it was solved by the method above.What method is right?

 

[voko]

To convince yourself that the method leads to the correct result, you could consider the left and right parts of the plank, and the torques thereof, separately.

 

[adjacent]

how can i consider the torque of the right part?Please look at the diagram

 

[voko]

You know the lengths of both parts. You know the material is uniform.

 

[Doc Al]

Keep it simple. There are two forces to consider:
- the weight of the plank. Where does it act?
- the weight of the attached object. Where does it act?

Compare the torques created by these two forces.

 

[adjacent]

my question was: the weight of the plank act in the center of gravity but one part of the plank is on other side.so the whole weight could not act on the right part,there should be some force on the left side as well

 

[adjacent]

for example the a plank is on a pivot and the plank's center of gravity lies on some side so the torque on that side is greater than the other side.it is not sensible to assume that there will be no forces on the other side?

 

[Doc Al]

my question was: the weight of the plank act in the center of gravity but one part of the plank is on other side.so the whole weight could not act on the right part,there should be some force on the left side as well

Gravity acts on the entire plank, of course. But, for the purposes of force/torque analysis, you can treat the plank as if all the weight acted at a single point: The center of gravity.

You can certainly divide the plank up into two pieces, one on the left of the pivot and one on the right. Then you can find the weight of each piece and figure out its torque and so on. But, you'll end up with the same answer as if you just treated the entire weight of the plank as acting on the full plank's center of gravity. That's the beauty of the concept of center of gravity. It really simplifies things.

 

[adjacent]

Thanks Doc Al.The laws of physics is just amazing.