Amount of work in displacing a brick

[rudransh verma]

ou understand why we take the position of COM and why only the difference in height of the COM is what matters? (

please do explain.

 

[Delta2]

The detailed answer is more mathematics than physics and is using integral calculus, maybe there is this explanation in your textbook.

In short we can consider that the mass of a rigid body is all concentrated at the COM position in a single material point and do the work calculations like we have a single point.

It is only the difference in height that matters because the work is actually an integral of a dot product of the weight and the displacement, and because the weight we consider it to be pure vertical, all that matters is the vertical displacement, that is the difference in height.

 

[rudransh verma]

The detailed answer is more mathematics than physics and is using integral calculus, maybe there is this explanation in your textbook.

It is in future chapters. Right now its work,energy and circular motion.

 

[rudransh verma]

It is only the difference in height that matters because the work is actually an integral of a dot product of the weight and the displacement, and because the weight we consider it to be pure vertical, all that matters is the vertical displacement, that is the difference in height.

Can I say because the gravity is conservative in nature so its work depends only on the initial and final points not the path taken by the COM?

 

[hutchphd]

The reason it is really useful here is that the center of mass (and hence gravity) for a uniform body with nice symmetry is easy to figure out. In this case it is just the "center" of the brick. For slightly more complicated shapes one often remembers the location.

 

[Delta2]

Can I say because the gravity is conservative in nature so its work depends only on the initial and final points not the path taken by the COM?

Yes . To be a little bit more accurate it depends only on the potential energy of the initial and final position. That's why @caz instructed you to find the potential energy.

 

[Frabjous]

As an exercise, write down an equation for the gravitational potential energy of the brick in your problem.
Hint: It involves a simple integral over the volume of the brick.
Hint2: How would you calculate the mass of the brick using a constant density and an integral? Think about why this works.

 

[rudransh verma]

To be a little bit more accurate it depends only on the potential energy of the initial and final position.

I mean since the work is conservative in nature so W12=-W21 where W12 is the work from traveling from point 1 to 2. And any path taken by the body results in same W since in conservative forces W does not depend on distance but displacement of the body.

 

[Delta2]

I mean since the work is conservative in nature so W12=-W21 where W12 is the work from traveling from point 1 to 2. And any path taken by the body results in same W since in conservative forces W does not depend on distance but displacement of the body.

Be a bit careful on how you express yourself, I don't think I have heard the term conservative work but rather i have heard work of conservative force.

Also in conservative forces the work doesn't depend on the path but on the initial and starting positions. This is a consequence of the gradient theorem of vector calculus.

 

[Frabjous]

Where is this problem from? If it is from a book, include the edition.

 

[rudransh verma]

Where is this problem from? If it is from a book, include the edition.

It’s a book you will never find. So stick to my postings in future. (Narayans AIEEE crash course vol.1)