The conservation of energy applying to TWO objects

[flyingpig]

Homework Statement

http://www.collegeboard.com/prod_downloads/ap/students/physics/ap04_frq_physics_cm.pdf

Question 2 part c)

"Calculate the rotational inertia of the pulley"




Answer Key: http://www.collegeboard.com/prod_downloads/ap/students/physics/ap04_frq_physics_cm.pdf

The Attempt at a Solution

Something about the alternative solution makes no sense to me

½m(v² - v₀²) + mg(h - h₀) + ½I(ω² - ω₀²) = 0

½m(v² - 0) + mg(0 - D) + ½I(ω² - 0) = 0

-mgD = -½Iω² - ½mv²

Now here comes the problem the solution said the kinetic energy is the CHANGE for the block, not the pulley, so how come when I is solved, it is assumed that I is for the pulley? Since the energy is calculated for the CHANGE for the block and not the pulley.

 

[kuruman]

The links don't work for me. Maybe they work for someone else.

 

[flyingpig]

It's on collegeobard AP Physics C 2004 EXAM

 

[kuruman]

It's on collegeobard AP Physics C 2004 EXAM

OK, but this is no link. If you are requesting our help, you should make it easy for us to provide it.

 

[flyingpig]

OK, but this is no link. If you are requesting our help, you should make it easy for us to provide it.

Here is the general link http://www.collegeboard.com/student/testing/ap/physics_c/samp.html?physicsc

I don't know why it isn't working.

 

[flyingpig]

please help...

 

[Doc Al]

Now here comes the problem the solution said the kinetic energy is the CHANGE for the block, not the pulley, so how come when I is solved, it is assumed that I is for the pulley? Since the energy is calculated for the CHANGE for the block and not the pulley.

Only the block changes its gravitational PE, but both the block and pulley change their kinetic energies. The decrease in the block's PE equals the increase in total KE. It's total mechanical energy that is conserved, not just the energy of the block.

 

[flyingpig]

Only the block changes its gravitational PE, but both the block and pulley change their kinetic energies. The decrease in the block's PE equals the increase in total KE. It's total mechanical energy that is conserved, not just the energy of the block.

But shouldn't I be both the pulley and the block, not just the pulley alone?

 

[Doc Al]

But shouldn't I be both the pulley and the block, not just the pulley alone?

What do you mean by 'the pulley alone'? The conservation of energy applies to both together.

 

[Doc Al]

But shouldn't I be both the pulley and the block, not just the pulley alone?

I think I see what you're asking now: Why should the rotational inertia (I) apply only to the pulley? Well, the pulley is the only thing rotating. The pulley rotates but doesn't translate, so it has rotational KE only; the block translates but doesn't rotate, so it has translational KE only.

 

[flyingpig]

I think I see what you're asking now: Why should the rotational inertia (I) apply only to the pulley? Well, the pulley is the only thing rotating. The pulley rotates but doesn't translate, so it has rotational KE only; the block translates but doesn't rotate, so it has translational KE only.

Is it possible to break the equation into two parts? One for the conservation of energy for the pulley and one for the block? Can you show me if is possible?

 

[Doc Al]

Is it possible to break the equation into two parts? One for the conservation of energy for the pulley and one for the block? Can you show me if is possible?

I would not recommend that. To apply conservation of energy to the block alone, you'd have to consider the work done by the external force of the rope.

Applying conservation of mechanical energy to the system as a whole is the easy way, since no external work is done on the system.

 

[flyingpig]

Wait, I just thought of a better solution, but I am not sure how it works mathematically or is it even right.

Since the block isn't rotating, no moment of inertia exists?

 

[Doc Al]

Since the block isn't rotating, no moment of inertia exists?

It has a moment of inertia, but it's irrelevant since the block isn't rotating. As I said in post #10, the block has no rotational KE.