# Transfer of momentum

PBE6
Posers and Puzzles 18 Oct '06 19:33
1. PBE6
Bananarama
18 Oct '06 19:33
I was just musing about this...if you have an one object that is significantly larger than another, and you crash the first one into the second one, the second object gets a significant velocity boost. Just doing a quick calculation - assuming an elastic collision, m1 = 10 x m2, and v2 = 0, the resultant v2 is about 1.8 times the initial v1. If you set up a series of masses, you could theoretically accelerate a small projectile to a high speed with a relatively small set of intermediate projectiles. Does this ever get used in the real world? Or does the inelasticity of most collisions render this process useless?

Geez, I'm starting to sound like sonhouse...
2. 18 Oct '06 20:14
I think what you're saying isnt really true. You pretend like a set of objects could accelerate a smaller (ie less heavy) object more than just one object could. It's not true because this is (for what i know) just a case of no energy can be lost (I don't know the proper English term, but you know what i mean). Thus the larger object gives all his kinetic energy to the smaller object, which gets a higher velocity because of the formula E=½mv². E remains constant, m gets larger so v² has to be bigger and so does |v|.
I'm sorry if i misinterpreted your statement.
3. 18 Oct '06 20:23
Originally posted by Darrie
I think what you're saying isnt really true. You pretend like a set of objects could accelerate a smaller (ie less heavy) object more than just one object could. It's not true because this is (for what i know) just a case of no energy can be lost (I don't know the proper English term, but you know what i mean). Thus the larger object gives all his kinetic ene ...[text shortened]... arger so v² has to be bigger and so does |v|.
I'm sorry if i misinterpreted your statement.
That sounds right. Two objects are all that is needed as with a cricket bat and ball etc,
4. PBE6
Bananarama
18 Oct '06 20:53
Originally posted by Darrie
I think what you're saying isnt really true. You pretend like a set of objects could accelerate a smaller (ie less heavy) object more than just one object could. It's not true because this is (for what i know) just a case of no energy can be lost (I don't know the proper English term, but you know what i mean). Thus the larger object gives all his kinetic ene ...[text shortened]... arger so v² has to be bigger and so does |v|.
I'm sorry if i misinterpreted your statement.
That's not what I'm saying at all. Let me explain with a few simple scenarios and quick calculations...

Trial #1: Two objects only

m1 = 10 kg
m2 = 0.1 kg
v1i = 10 m/s
v2i = 0 m/s

v1f = 9.80 m/s
v2f = 19.80 m/s

Trial #2: Three objects in series

m1 = 10 kg
m2 = 1 kg
m3 = 0.1 kg
v1i = 10 m/s
v2i = 0 m/s
v3i = 0 m/s

v1f = 8.18 m/s
v2f = 18.18 m/s

and after m2 crashes into m3,

v2f = 14.88 m/s
v3f = 33.06 m/s

As you can see, in the first scenario the 0.1 kg object attains a velocity of 19.80 m/s, and in the second scenario the 0.1 kg object attains a velocity of 33.06 m/s. In order for the two-object scenario to produce the same final velocity for the 0.1 kg object as the three-object scenario, the 10 kg object needs to be moving at approximately 16.70 m/s initially. There is no way to produce the same final velocity for the 0.1 kg object in the two-object scenario by increasing the first object's mass alone (the maximum velocity of the 0.1 kg object after one collision will be twice the first object's initial velocity, independent of its mass).

The trade-off here is between (a) the first object's velocity; and (b) the number of stages (i.e. complexity and mass) of the system. I was just wondering if there's ever a situation where changing (a) is unfeasible and changing (b) is the only solution. Does anyone know any situations like that?
5. AThousandYoung
All My Soldiers...
18 Oct '06 21:291 edit
I'm having a tough time thinking of such a system. Why do we want to send small objects moving at high speeds?

Weapons, for one, but we don't use collisions to send projectiles off at high speeds.

Subatomic particle accelerators? I don't think collisions are used here either (to accelerate the particles that is).

It seems to me that any time we want to accelerate small objects we use other methods except in ball and stick games.

Communication? EM radiation works so much better.
6. 18 Oct '06 22:22
Originally posted by PBE6
That's not what I'm saying at all. Let me explain with a few simple scenarios and quick calculations...

[b]Trial #1: Two objects only

m1 = 10 kg
m2 = 0.1 kg
v1i = 10 m/s
v2i = 0 m/s

v1f = 9.80 m/s
v2f = 19.80 m/s

Trial #2: Three objects in series

m1 = 10 kg
m2 = 1 kg
m3 = 0.1 kg
v1i = 10 m/s
v2i = 0 m/s
v3i = 0 m/s

v1f = 8 ...[text shortened]... easible and changing (b) is the only solution. Does anyone know any situations like that?[/b]
I see your reasoning now. I think your method is very unpractical. If i wanted to launch an object by using a larger object I would place the smaller object against a thin plate, which is kept in place good enough to entirely stop the larger object, such that all energy from the larger object will go to the smaller object (apart from some friction etc.). The use of more objects in your example is just to make sure (for what i can tell) that more of the kinetic energy from the large object goes to the small object. Can someone show what happens if you take infinite objects who differ nearly nothing in mass?
ie x1=m
x2=m+dm
x3=m+2dm
xn=m+ndm
or xn=x(n-1)+dm
I dont know if i defined this sequence properly, but i think the idea is clear now.
7. PBE6
Bananarama
19 Oct '06 03:42
Originally posted by AThousandYoung
I'm having a tough time thinking of such a system. Why do we want to send small objects moving at high speeds?

Weapons, for one, but we don't use collisions to send projectiles off at high speeds.

Subatomic particle accelerators? I don't think collisions are used here either (to accelerate the particles that is).

It seems to me that any time ...[text shortened]... methods except in ball and stick games.

Communication? EM radiation works so much better.
I agree, there aren't any systems I can think of where you'd need to use a series of smaller, slower weights...you just get bigger, faster ones! Maybe on the geek version of Survivor, the one where the contestants don't kill each other in a race war.