# Difference between momentum & KE. Please, help.

1. Feb 20, 2013

### manuka

two days of searching and reading and still i can not comprehend these concepts.

what i know:
1)momentum is vector and energy is scalar. Well it gives no intuition to me.
2)i know that Force x dTime is change of momentum. This really make sence.
3)i know that Force x dDistance = KE This makes sence too.
4)i know that momentum and kinetic enegry are like space and time.. One acts in Time the other acts in space.
5)i know two objects can have same momentum and different KE. This does not help my intuition...

I can't even formulate the question... I mean .... eh.... well that is THE difference on the INTUITION level?
Maybe my question is wrong by its own nature? Maybe i need not Differentiate them but to UNITE?
If so... how to get intuition about their influencing each other (how KE "flows" into MV and vice-versa)?

subquestion:
if i apply force=1N for 1min of time to some Object
AND OBJECT does not move AT ALL (i.e. friction is to strong)

then i have
I=F(t1-t2)>0.

BUT this equation
F(t1-t2)=m(v1-v2)
can not hold, because (v1-v0)=0 AND F(t1-t2) >0
There is a mistake in my resoning! I can't find it. Help!!!

Last edited: Feb 20, 2013
2. Feb 20, 2013

### Staff: Mentor

Then you have another force acting on the object, don't you?

3. Feb 20, 2013

### manuka

yep. Friction acts on it.... and.... well..... emmm.... and I push it...

So friction Force and Push force will cancel out.
I understand. But THE EQUATION :) ....

Oh, i got it. Are you telling me that here:
Ft=m(v1-v0)

F-should be the SUMM of all forces :) , and not only one of many forces?

Hhhhhm. Well, i guess you helped me with "subquestion" but i need some time to digest. Thanks.

4. Feb 20, 2013

### Staff: Mentor

Exactly!

In your reflexion, remember also that KE = P2 / 2m

5. Feb 20, 2013

### manuka

well i've seen this formula KE = P2 / 2m
But... it does not click.

You know i've been struggling with concept of FORCE and momentum for some time and it clicked like this:
Once you face a problem of mesuring motion then you undestand that Newton was right and MxV is a great definition.
Then meaning of force comes naturally once you understand that it's just a rate of change of Momentum...

But it never clicks in momentum & KE question... I feel that answer lies in time and distance relation (i mean NOT the relativity stuff).

I've heard some one said:
That quote:
Is a mistery for me.

Last edited: Feb 20, 2013
6. Feb 20, 2013

### Staff: Mentor

For me too! Don't read too much into it. The more problems you solve, the more the concepts will become familiar.

7. Feb 21, 2013

### manuka

Will this statment be true?

Momentum is a measure of how much FORCE is needed to stop an object.
Kinetic energy is a measure of how long(TIME) an object can resist to a stopping FORCE.

It's like this analogy:
Car Engine size is like a momentum, while fuel tank is like kinetic energy.
The bigger( more powerful) the engine is, the more FORCE it can produce (and thus the more force needed to stop it).
The more fuel in the tank of a car, the longer it can resist stopping FORCE.

well this ALMOST clicks :) but there is small issue here:
words "how much Force" ... it is a qualitative definition... how we can give quatative definition of "much force"?

Should we use Ft or Fs?
Cause both give some measure of quantity of the FORCE just from different perspectives.

8. Feb 21, 2013

### Staff: Mentor

I think I'm getting a better understanding of what is meant here. Conservation laws come from symmetries: conservation of momentum (energy) is a result of the fact that the laws of physics do not change if you translate the origin of space (time).

I'll think a bit more about your analogy using forces and come back to you.

9. Feb 21, 2013

### jbriggs444

That is not correct.

Momentum is a measure of how long (TIME) an object can move while subject to a fixed retarding force. Kinetic energy is a measure of how far (DISTANCE) an object can move while subject to a fixed retarding force.

If you double an object's speed, it takes twice as long to bring it to a stop. Twice the momentum. During this (doubled) time it is moving twice as fast so it takes four times as much total distance to stop. Four times the energy.

That's why momentum is proportional to velocity while energy is proportional to the square of velocity.

Use a cable with a force gauge on it to pull on the car you're thinking about. If the gauge reads 20 pounds, that's 20 pounds of force. If you want to convert that to momentum or energy, use a stop watch or a tape measure.

10. Feb 21, 2013

### manuka

jbriggs444, Thanks for help, but it do not click.

about truck... what if we talk about shots fired at a deer for example.
Bl=light bullet; mass 1kg, velosity 100km/h
Bh=heavy bullet; mass100kg, velocity 1km/h

so moments are equal, but KE is different (and the difference is huge).

1................................
Bl while hitting deer body will suffer from deer tissue friction
Bh while hitting deer body will suffer from friction too.

so bl and bh are symmetrical in this case.

2................................
Bl will pass through body cause it can generate much work (i.e. it can apply FORCE over DISTANCE of a deer body)(so fuel tank is full and used to pass through tissue)

Bh on the other hand will have no "capacity to apply Force over space" (i call it: fuel tank is empty), and it will just pucs the deer back (a little)
3................................
now KE situation is clear.
but momentum is not.
Bl will not be able(almost) to transfer moment to a deer? It will transfer motment only to a fraction of deer tissue?
Bh will transfer moment to a whole deer body?

well there is some trick... I mean that bullet should SHARE momentum with the body it impacts.
Bl can not share it with enough mass and pass right trough. While Bh finds alot of mass to share momentum.?

Last edited: Feb 21, 2013
11. Feb 21, 2013

### Jano L.

Perhaps you seek the understanding that only comes with solving many problems in mechanics.

One great difference between momentum and kinetic energy of body in mechanics is that momentum is always conserved, while energy can dissipate into heat and other hidden forms. Good example is the method of measurement of how fast bullets move. Shoot a bag full of sand, suspended on a wire:

http://en.wikipedia.org/wiki/Ballistic_pendulum

In this experiment, the deviation of the bag depends on the momentum only. It can be light and fast or slow and heavy, the momentum is the determining thing.

On the other hand, if you are interested what is the minimum amount of fuel you need to get something into motion, the important thing is always kinetic energy, since you transform energy of fuel into the energy of the body.