# Kinetic energy vs. momentum

1. Aug 29, 2014

### Javiatrix

Beginner and first time poster here so be gentle!

First off, I understand the main difference is that one is an energy and one is a vector, but can somebody explain the following -

A car of mass 1000 kg is travelling at 30 m/s.
KE = 450 kJ
Momentum = 30,000 kg m/s

The driver brakes the car down to 15 m/s .
KE = 112.5 kJ
Momentum = 15,000 kg m/s

Which all makes sense mathematically, as KE varies quadratically with speed, so halving the speed quarters the KE, and as momentum varies linearly, halving the speed halves the momentum, BUT -

I was always told that momentum was effectively how much 'umphh' something has. But if halving the speed requires the brakes to absorb 75% of the car's KE in this case... Isn't 'umphh' kinetic energy's job??

*Feeling baffled!*

2. Aug 29, 2014

### Staff: Mentor

Hi Javiatrix, welcome to PF!

Since "umphh" is a very vague term I am sure that you could take it to mean either.

If you consider a perfectly plastic collision, the change in the object's momentum determines how much the object gets pushed around and the change in the system's KE determines how much the objects get damaged. "Umphh" could refer to either.

3. Aug 29, 2014

### RyanXXVI

"Umph" is a very obscure term, especially in physics. Do you mind clarifying?

4. Aug 29, 2014

### A.T.

No, it's more like 'wham'.

5. Aug 29, 2014

### sophiecentaur

I would recommend that you challenge the person who was 'always telling you' that as to what he / she* meant by the term. Don't try to reconcile what you can learn about what happens in collisions with such a vague statement - don't bother. Just learn about it from the accepted theory and you won't (shouldn't) be baffled.
* Probably not a 'she'; 'she's tend to avoid such BS terms!

6. Aug 29, 2014

### Staff: Mentor

'umphh'

Momentum is just a useful currency. It's the KE that gives a projectile its punch.

7. Aug 29, 2014

### sophiecentaur

I agree. A fairly heavy mass, dropped on your foot may hurt a bit but a bullet with the same momentum can mess it up completely.
But you can't easily work out the result of collision using just the Kinetic Energy situation.
Horses for courses. (In French cuisine sometimes)

8. Aug 30, 2014

### Javiatrix

Thanks for the replies all!

Sophie, I'm not an admirer of BS terms either ;) But I figured such a loose connotation would inspire the debate that would lead to some kind of answer!

Momentum as a "useful currency" is the best starting point I could come up with in my mind, and using it is not a problem, but what I struggle to get my head around is how one varies as the quadratic of the velocity, and one as the linear. That's a BIG difference for two items that appear to be so closely related.

It's the concept that removing 75% of something's KE is equal to removing only 50% of its momentum in this case, for example, that I'm struggling with.

I wish I was one of those people who just accepted what they're taught, but unfortunately I'm cursed with taking everything apart and examining it because that's how my mind makes solid ground out of it!

Edited to say - maybe my problem is trying to 'over-understand' something that's dimensionless and manmade as a "currency", useful only due to the units it combines?

9. Aug 30, 2014

### maheshshenoy

Hello Javiatrix

"My first post too :D"

I wouldn't say momentum is just a cooked up "currency" to work with physics.. I think of momentum as something that defines how much "motion" an object has. Because, when objects bang into each other, collide, break apart, plough, or even explode, the "motion" gets transferred, but not destroyed, thus momentum is very real and not just dimensionless and man made.

Energy is real too, but the problem with energy is, there are other kinds of energy than just the "energy of motion" , hence in any of the event described above, although the total energy cannot be destroyed, "energy of motion" can be converted into something else (heat).. (which is not the case with momentum).

Bottom line is .. Momentum tells u about how much "motion" an object has..
Kinetic energy basically tells u "how much work u did to acquire that motion" (or how much work u have to do , to destroy that motion)

To throw a ball with twice the momentum u have to throw with twice the speed .. but to do that, u end up having to do 4 times the work, thus to achieve twice the momentum, you had to do four times the work, hence u end up with 4 times the k.e. (and vice versa, when u are stopping a ball maybe )

10. Aug 30, 2014

### mal4mac

My "naive physics" image of kinetic or potential energy is "ability to do work". Think of a large furniture delivery man on coffee break - a lot of "potential energy". Now visualise him shifting furniture - lots of "kinetic energy". in either case plenty of "ability to do work". To visualise momentum I see him, quickly, moving a piano at constant speed - don't get in his way - he has high momentum, an "ability to keep going".

I've never though of the noises he emits - 'umphh' sound like the noise he might emit when first picking up the piano - so it represents "dramatic conversion of potential to kinetic energy".

If it's a real heavy piano then the expostulations for momentum would be ongoing, e.g., "****, ****, ****" Where **** represents statements like "dear me", "ho hum", "tarry diddle",...

11. Aug 30, 2014

### sophiecentaur

The OP has, lurking inside it, a version of the Feynman 'Why' question. There is no percentage in looking for a reason for the difference between the two quantities or to ask why there is a difference in how they vary with circumstances. They are both, after all, mathematical formulae and, not surprisingly, they produce different answers for the same inputs. They are not mutually exclusive. You are a test pilot and a piano player - no contradiction there, unless you approach the situation, expecting piano players can't fly.
The question about the properties of moving objects was one of the earliest to be considered in Physics. The properties of an object in motion can be expressed both ways and, for a long time, the two were treated as equivalent. The question resolved itself when it was appreciated that one (the KE), relates to the work done in getting it to go that fast, which is the Force times the distance over which it's applied whilst the other (Momentum) relates to the Force times the time for which it's applied.
Obviously, work is done when the Momentum is increased but Momentum is a quantity that is 'Conserved' between the mass and the object that is pushing it. If you consider the KE situation before and after, then you can't expect it to be conserved. Elastic collisions are impossible.

When there is the choice between the mathematical description and the hand waving / jargon description, you really have to choose the maths and then find a way of reconciling the other explanation with it. Maths, after all, is just a language and happens to be a more successful one for Science. If you were to compare modern English with ancient Latin for describing scientific processes, you would find Latin was sadly lacking - if only because of the limited vocabulary. The vocabulary of Maths is even better than what's available in English. There is no reason to think that mathematical descriptions are a cop out - if anything, it is often the verbal (maths-less) description that limits ones understanding.

12. Aug 30, 2014

### mal4mac

Please don't use "u" for "you", it's liable to be insanely confusing in this context!

13. Aug 30, 2014

### dean barry

Sounds like momentum deals with exclusively mass and velocity, whereas energy can be kinetic, potential etc.
Maybe they deal with seperate types of problem.
The bullet into the block hanging by a string is a classic, use momentum conservation to calculate the final velocity after collision, then KE to PE to figure the height reached by the block.
maybe
comments ?

14. Aug 30, 2014

### sophiecentaur

I agree. If someone wants to be precise about the Physics, the least they can do is to be precise in their language.
Yes. That is a reasonable way to look at it. You can only transfer momentum into momentum elsewhere but KE can easily become PE.

15. Aug 30, 2014

### Javiatrix

Thanks for all the excellent replies; at my early level it's much clearer for me to treat the two as the separate entities that they are, more precisely that momentum is reserved for exactly what's written in the simple formula (mass and velocity), and energy as a way of describing something different, which removes my initial confusion. I'm just starting an engineering degree and as it's been a few years since I left school, I'm sure a lot of it will come together and I'll bridge the broken links again as I gain a more rounded knowledge of these subjects.

I'm not sure I'll be a lot of help myself yet when it comes to answering questions, but this looks like a good site so long as one can filter out the garbage (internet 101!), and I hope to show my face around in the future :)

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