View Full Version : Kinetic energy & momentum

1st Jan 2014, 16:58
I'm hoping someone can help me with my confusion here...

I was looking at an internet site about rifles & apparently when fired, the bullet & rifle share the same momentum, but the bullet gets something like 95% of the kinetic energy, so clearly, kinetic energy & momentum are not the same thing.

I imagined a standard old .303 being fired (For arguments sake disregarding the ejecta of the cordite & air resistance etc) & another empty but identical rifle 'Catching' the bullet in its barrel.

Here is the problem... If the firing rifle kicks back at for example 10 feet per second, but only absorbs 5% of the energy of the bullet, which may be travelling at about 2000 feet per second. It seems that there must be some energy 'Lost' somewhere if the catching rifle must 'Kick back at 10 feet per second, in order to maintain the conservation of momentum.

I can imagine a great deal of adiabatic heating of the air in the catching rifles barrel, is this where the excess bullet energy goes? If done in space, would the bullet liquefy in order to dissipate this unequal energy?

I find that there is plenty on the net about kinetic energy & momentum, but it usually just tells you how to work out momentum as 'Velocity times mass' & kinetic energy as 'Half mass times velocity squared'

Which doesn't really answer my rifle analogy.

I'm assuming here that if you fire a rifle at me & I catch the bullet in my rifle, I'll feel the same 'Kick' as you, but our respective rifles have no where near the energy of the bullet.

I feel a bit of an idiot for having to ask such a basic question, but it's bugging me.

1st Jan 2014, 18:00
You've got the right idea.

Taking your .303 as the example.

SMLE rifle mass m1= 4 kg
180 gr bullet mass 12g, m2= 0.012 kg, muzzle velocity v2 = 783 m/s

Conservation of momentum means m1v1 + m2v2 = 0, so v1 = -2.3 m/s

The firing rifle recoils at at initial velocity of about 5 mph.

kinetic energy of 0.5mv^2

bullet k.e. = 3680 J, rifle k.e. = 11 J

The bullet has 99.7% of the kinetic energy.

Estimated energy released by the gunpowder (48 grains max = 0.003 kg) x 3 MJ/kg = 9 000 J

so about 41% of the energy goes into kinetic energy, with almost all the rest as heat and pressure energy of the gases.
The explosion is very rapid so there is proportionately not much heating of the cartridge or rifle.

The key points for all collisions are:
momentum (only 1 type) is always conserved
Energy (many types) is also conserved, but may be transferred from one form to another.

When the bullet is caught by the second rifle, assuming no loss of velocity until it hits the catching rifle's breech, then the catching rifle will indeed recoil at about 2.3 m/s(5mph, 10 fps) as the bullet slows.

However, the 3680 J of bullet kinetic is transformed into 11 J of kinetic energy of the catching rifle/bullet and 3669 J of some other kind(s) of energy.
I would imagine most of this energy is deformation energy, changing the shape of the bullet and breech (and maybe shattering one or both), with some heating. The bullet slowing is again very rapid, so I would imagine it deforms, but it would only take 733 J to heat up and melt the bullet. This is only 733/3680*100 = 20% of the available energy, so possible.

I would not suggest trying this at home, but the accepted method is to buy a redneck a six pack of beer, then tell him it's impossible :E

1st Jan 2014, 18:42
Thank you Fox3, I could not have hoped for a better & more concise answer to my question.

The internet just seems so full of muddle, without such good explanations.

1st Jan 2014, 20:04
The internet just seems so full of muddle, without such good explanations.

If you want the best answer, ask a professional. In my experience, you'll find loads of them on Pprune. Physics explanations is my little party piece.

Fox3, MInstP

2nd Jan 2014, 14:15
This thread is awesome.
Fizzicks rocks

2nd Jan 2014, 19:24
I do have another physics question that has been bugging me, but will need time to couch the question properly to its roots, as it were.

It's about the squaring of velocities & the speed of light. One can't just square a velocity & say "OK, I'll get there in a certain amount of time.

Using a single set of units is OK for just giving answers, but units of whatever source are man made things.

I can look up on the internet the energy of contained in one gram of matter in joules/metres per second etc in regard to the speed of light.

From a layman's point of view, it would add greatly to understanding if other calculations were given as an example in other units.

I've read a number of books about relativity & all that, catch glimpses of understanding at times, but it seems infuriating at other times.

I still think that 'Getting the right answer' from a standard set of units, is a sort of 'Shortcut' bereft of a proper understanding.

Given that nothing can travel faster than light, the velocity squared thing, seems a strange concept, a bit of mathematical trickery if you like.

The trouble with me, is that I like to understand the concept behind things, rather than giving a parrot fashion answer in Ergs or whatever.

Just musing here, but as ever, grateful for any insight.

PS, was going to wait & get the question nailed down properly, but my fingers ran away with me.

2nd Jan 2014, 21:40
Momentum and energy are quite different. Momentum is conserved because of the spatial symmetry of Mr Newton's Universe. Energy is conserved because of the time symmetry.

In relativity, the difference between the squares of the energy and momentum are related to the square of the mass of the object that possesses them, adding another level of richness.


Subject to the bullet slowing on its trip, you get the same momentum from absorbing a gunshot as the shooter would get from the recoiling rifle, if he allowed it a run up to his shoulder. In fact, it tightly held, the Earth gets the recoil, rotating very slightly in the opposite direction to that in which the bullet flies.

2nd Jan 2014, 22:26
FI - Natural Units (http://en.wikipedia.org/wiki/Natural_units), see Planck units in particular, would likely satisfy your niggle.

Not that it makes a huge difference in anything other than our ability to easily conceptualise things like a metre, a kilogram or a second. Since you can convert metres to Planck lengths (1.61610^−35 m), kilos to Planck masses (2.17610^−8 kg) and seconds to Planck time (5.391210^−44 s) then the numbers mean the same thing, they're just scaled up to human size rather than working on unimaginably small (or even large) scales (http://htwins.net/scale2/).

3rd Jan 2014, 21:00
Here's a thing: if you accelerate a mass to relativistic velocities (approaching the speed of light c), with a constant force, you have to include the effect of "mass dilation". If F = m a, and F is constant, what's to stop the mass accelerating indefinitely past c? The acceleration has to tend to zero, which can only mean that the mass has to increase towards infinity as the velocity increases.

This page (http://www.phy.olemiss.edu/HEP/QuarkNet/mass.html) gives a formula and a sample calculation: a mass that starts at 5g now, accelerated to 0.95c will then have a relativistic mass of 16g.

Particles speeding around the Large Hadron Collider are getting much closer to c than that, giving them much higher mass, momentum and energy. Which, as this page (http://lhc-machine-outreach.web.cern.ch/lhc-machine-outreach/lhc-machine-outreach-faq.htm) describes, explains why the LHC has to be so Large, and its sensors so solid. :8

3rd Jan 2014, 21:32
Flight Idle - I can't explain Relativity in a forum post, but a good starting point is as follows.

Consider the equation velocity = distance / time.
At normal speeds, we are used to different observers (say, the driver of a car and a pedestrian watching the car going past) agreeing on time. Their watches will both read the same.
It turns out that at high speeds, this is noticeably not true. We're tried sticking really accurate atomic clocks in aircraft and spacecraft, and the faster a clock travels, the slower it appears to run to people on the ground. When the moving (slowed) clock gets back on the ground, it seems to keep time at the same rate as a grounded clock again, but preserving the error which built up whilst it was moving fast.
We find the one thing that is agreed on by observers at different speeds is the velocity of light in a vacuum, each using the rulers and clocks available to them. It follows that if they disagree about time, they must disagree about length by the same factor in order for velocity of light = distance/time to work.
Similar effects happen for mass increase with speed, etc.

How's that for starters?

3rd Jan 2014, 21:44
From the depths:

It follows that if they disagree about time, they must disagree about length by the same factor in order for velocity of light = distance/time to work.

Lorentz and stuff?


3rd Jan 2014, 22:01
Lorentz is the factor, yes.

4th Jan 2014, 08:28
Thank you again Fox3.

I must re-read my books again. My point is that one can't square a particular speed to arrive at another one.

It can't actually be a physical thing. If I was travelling in my car at 10 mph, just squaring that would = 100 mph.

If travelling at exactly the same speed, but using feet per second, or furlongs per fortnight as units instead & I squared those. I would end up with different answers, not the equivalent of 100 mph

So, squaring speeds is just a mathematical concept.

The problem with googling, 'What is the energy equivalent in one gram of matter' is that one just gets worked examples in SI units.

I did 'Just about get it' once, but it's evaporated from my mind.

As has been suggested, an open university course may be a good idea!

4th Jan 2014, 09:34
My point is that one can't square a particular speed to arrive at another one.You are right, you can't.

But not because of the value part, but because a speed squared is no longer a speed.

If you square a speed that is no longer a speed but speed-squared. If you square a length you don't get a length but a length-squared, which is easy to interpret as an area. Speed-squared has no such simple physical meaning but works the same.

10miles/h squared is 100miles^2/h^2. So one hundred square miles per square hour.

10miles/h equals 14.67ft/s. Square that and you get 215.21ft^2/s^2. Square feet per square second. To convert that back to miles per hour you need to apply the relevant factors twice each. 5280 feet to the mile and 3600 seconds to the hour gives you back your 100 square miles per square hour.

All is well.

4th Jan 2014, 09:34
Well, I did my physics degree with the OU :ok:

4th Jan 2014, 11:36
Well, I did my physics degree with the OU