# Mass/Energy and Inertia

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1. Oct 31, 2014

### mokeejoe5

If you trap a lot of energy in a box does the system (box plus its contents) gain inertia and become more difficult to accelerate?

2. Oct 31, 2014

### Staff: Mentor

Yes.

3. Oct 31, 2014

### mokeejoe5

So there's nothing special about mass then? its just concentrated energy in a small volume?

4. Oct 31, 2014

### Dr.D

How did you trap all that energy in the box?

5. Oct 31, 2014

6. Nov 5, 2014

Gyroscope!

7. Nov 5, 2014

### Dr.D

Well, I have to admit, that makes as much sense as the original proposition.

8. Nov 5, 2014

9. Nov 5, 2014

### mtworkowski@o

I knew you would like it. Kinetic energy raising inertia and causing the box to behave differently than if it were stationary.

10. Nov 5, 2014

### Khashishi

The answer is yes, but you can show this yourself, rather than take our word for it. Try a thought experiment where you have one object made out of two atoms of given mass. Calculate the kinetic energy of the atoms when you translate the whole object. Now heat up the object (give the atoms some initial and opposite kinetic energy). Now calculate the kinetic energy when you translate the whole object.

11. Nov 5, 2014

### mtworkowski@o

I used to cut allot of classes. I'm sure i missed that one!

12. Nov 6, 2014

### A.T.

What does this have to do with an increase in inertia? How does it apply to energy stored in a spring?

13. Nov 6, 2014

### Dr.D

I second that question: What does this have to do with an increase in inertia?

14. Nov 6, 2014

### mtworkowski@o

Yeah, i missed the logic on that one. But that happens sometimes.

15. Nov 6, 2014

### sophiecentaur

Perhaps it would be an idea to define what you mean by "inertia' in this context.

16. Nov 6, 2014

### Khashishi

I skipped a couple steps, and hoped everyone would still be able to follow. Let me elaborate some more.

The work it takes to move an object is equal to the difference in kinetic energy between the object at rest and the object in motion.
$W = T_f - T_i$
$F = dW/dx = dT/dx$
We can define a "mass" for the composite object using
$F = ma$
so
$m = \frac{dT/dx}{a}$
$m \propto \Delta T/\Delta v$

When you heat an object, the molecules gain vibrational energy. It takes more work to move a box of hot molecules than a box of cold ones. Let's simplify the composite object as much as is possible: it is composed of two atoms. When the atoms vibrate, they move in opposite directions so the total center of mass doesn't move. The kinetic energy of the object is simply the sum of the kinetic energy of the atoms, and any kinetic energy of any fields in the object (which we will assume to be zero).
Calculate the change in kinetic energy when you move the center of mass of the object. Do this for the cold object, and the hot object, and see which takes more work. The work it takes to move the object is proportional to the mass of the composite object.

17. Nov 6, 2014

### A.T.

The jack in the box has potential energy (in the compressed spring), that increases inertia.

18. Nov 6, 2014

### A.T.

I did. The change in kinetic energy is the same.

19. Nov 6, 2014

### Khashishi

Oh, you need to use the relativistic kinetic energy. Sorry about that.