# Question on momentum

1. Nov 27, 2004

### Ron77

Hi Folks,

Question on momentum.

I have been talking with someone who is more educated than I, especially in math, but they are saying something that just doesn't make sense to me. I do realize that physics doesn't always make 'sense' so thought I'd ask on here. He said I would need calculus to understand why, but the answer, almost seems intuitive...

Here it is..

He says that both of these will have the same momentum even though one has about 20 times the mass of the other and V is the same.

1) A person laying on their back does a bench press exercise with a real barbell weighing 200 lbs at a certain velocity

2) Another person laying on their back does a bench press exercise at the same velocity, but the resistance is provided by rubber bands that provide 200 lbs of downward tension. (like a Soloflex exercise machine)

I am thinking that number 2 will have almost zero momentum. It seems that no matter how fast you moved your arms, if you stopped, the 10 pound bar with the bands attached would 'stick to your hands' so to speak, but an actual weight would have the tendancy to 'keep in motion' moreso.

Also, I read that the definition of momentum is on the order of how hard it is to change the direction of an object. One could easily reverse the direction from travelling upward to downward if tension is provided by elastic materials, but if provided by a real weight with mass, it would be harder to change from upwards, to a downward movement... right?

Thanks,
Ron

Last edited: Nov 27, 2004
2. Nov 27, 2004

### krab

Your thinking is correct. So how does your friend define momentum if not mass times velocity?

3. Nov 27, 2004

### Ron77

I'm not sure, he said "Your using that formula?" Then said I needed to understand calculus for him to explain.
The only thing that throws me is he's one of the smartest and most knowledgable people I've ever met, so if we differ, I always assume he's right and I'm wrong.
This one just bugged me as I am usually far above average with mechanical and spacial problems, and I could almost 'feel' how momentum would be by just thinking about it..

4. Nov 27, 2004

### Astronuc

Staff Emeritus
Well, there is an equivalence between the two.

Define momentum as p = m v, where m is mass of the object in motion and v is the velocity.

But what is m, or rather the effect of m?

Let's define m as F/g, or the force, F, divided by the local gravitational acceleration.

Then p = F/g v.

F can be provided by mg or kx, where k = spring constant and x is the displacement, so if one could devise a way so that F/g = kx over the range of x, then they would have the same effective momentum.

so one could also say p = (kx/g) v.

As far as the person doing the work there is no difference.

In reality though, kx provides a variable force F, whereas mg is constant. I am not familiar with Soloflex and other systems so I am not sure show they compensate for this.

5. Nov 30, 2004

### ricemike

youre mathematically inclined friend is not in touch with physics
you re thinking is more correct than his.