# Homework Help: Milk jug inertia problem

1. May 22, 2010

### GreatEscapist

Our latest physics assignment was think-about-it-physics, not actual math physics.

1. The problem statement, all variables and given/known data
A milk jug sits on top of a sheet of paper. If this sheet of paper is pulled quickly from under the jug, the jug will not topple over. What explains this the best?

A. The jug has a lot of mass
B. The jug does not have a lot of mass
C. The jug has inertia
D. None of the above

2. Relevant equations

I wish there were equations to use...

3. The attempt at a solution

Well, long story short, my friend and I (Who were supposed to be working on this together) got in a huge argument over if it is C or D. (I'm pretty sure that those were the choices for A and B. The point is, they weren't the answer)

I put down D, because inertia just didn't sound/feel right. It probably is. She pointed out that inertia would hold it there, because inertia is *basically* the tendency of an object to resist changes in motion. So it wouldn't topple. But see, here's the thing- pulling something from beneath WOULD change its inertia. But does pulling it out faster make it so that it doesn't affect inertia?

I say D, because I think it's something else- I just don't know what it is. :tongue:

PLEEEEASE help me. I know it's easy, but we both over-analyze. Sucks for us.

2. May 22, 2010

### pgardn

THis is actually a little more complicated than it seems. But for an introductory class a short explaination... The jug has mass thus it has inertia. Inertia is the tendency to resist a change in motion (resist accelertion). So the jug "wants" to stay at rest. Removing the paper from underneath does not change the mass or the inertia of the jug.

The thing about this is the paper must be accelerated rapidly. If you just pull at a fairly constant velocity on the jug will stay right on top of the paper, so friction between the jug and the paper plays a role also. If you pull rapidly on the paper, then you "overcome" the force of friction which has the tendency to make the paper and jug stay together. Pulling the paper rapidly, again, has nothing to do with the inertia of the jug.

Maybe saying that there is an insignificant amount of friction between the jug and the paper would help the problem seem clearer. Trying this experiment with nice smooth silk v. gritty sandpaper, instead of paper, would show you that friction plays an important role.

3. May 22, 2010

### GreatEscapist

GAH! I was wrong. I hate that- so much. :grumpy:

Well, It did sorta make sense before when she said it was inertia. But that makes even more sense now.

4. May 22, 2010

### pgardn

Well it gets a bit more sticky also.

If the milk jug did topple it would be because of the torque exerted by the friction between the milk and the paper. It would cause the jug to actually begin to rotate. Once the jug rotated enough that its center of mass was not above the contact surface between the jug and the paper, it would topple due to gravity.

And then of course the center of mass changes as you pull the paper out as we have a liquid in the container. All these things are a bit messy in the real world so we try to make them simple situations by putting in what sometimes are unrealistic parameters to make sure we get rid of a lot of pesky variables.

Last edited: May 22, 2010