The conservation of energy applying to TWO objects

In summary, the problem involves finding the rotational inertia of a pulley in a system where both the pulley and block experience changes in kinetic energy and conservation of mechanical energy applies to the system as a whole. The block does not have a moment of inertia because it does not rotate, but the pulley does.
  • #1
flyingpig
2,579
1

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.
 
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  • #2
The links don't work for me. Maybe they work for someone else.
 
  • #3
It's on collegeobard AP Physics C 2004 EXAM
 
  • #4
flyingpig said:
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.
 
  • #6
please help...
 
  • #7
flyingpig said:
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.
 
  • #8
Doc Al said:
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?
 
  • #9
flyingpig said:
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.
 
  • #10
flyingpig said:
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.
 
  • #11
Doc Al said:
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?
 
  • #12
flyingpig said:
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.
 
  • #13
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?
 
  • #14
flyingpig said:
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.
 

Related to The conservation of energy applying to TWO objects

What is the conservation of energy?

The conservation of energy is a fundamental law of physics that states that energy cannot be created or destroyed, it can only be transferred or transformed from one form to another.

How does the conservation of energy apply to two objects?

In the context of physics, the conservation of energy applies to two objects when they interact with each other. This means that the total amount of energy before and after the interaction remains the same.

What are some examples of the conservation of energy in action?

Some examples of the conservation of energy in action include a pendulum swinging back and forth, a ball rolling down a hill, and a car engine converting chemical energy into mechanical energy to move the car.

What factors can affect the conservation of energy between two objects?

The conservation of energy between two objects can be affected by factors such as the mass, velocity, and type of interaction between the objects. Other factors like friction and air resistance can also play a role in the conservation of energy.

Why is understanding the conservation of energy important?

Understanding the conservation of energy is important because it is a fundamental principle that helps us understand and predict the behavior of objects in the physical world. It also allows us to design and improve technologies that rely on energy transfer and transformation.

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