Limitations in Experimentation?

[Crosshair]

Why doesn't the higher mass cart stop after hitting the lower mass object? Is this due to an imperfection in setting up the experiment? I was expecting that the equal and opposite force would completely cease the larger mass' motion.

http://http://physics.wfu.edu/demolabs/demos/avimov/bychptr/chptr3_energy.htm

 

[Nick O]

The link doesn't work for me, so I only have your words to go on.

Think of a train hitting a bird. The bird hits the train as hard as the train hits the bird; the forces are equal and opposite. But, the train has more momentum (mass times velocity) than the bird, so it keeps barreling along with no noticeable change in speed.

 

[Crosshair]

I apologize for posting a broken link, but you understood my question.

Great analogy. Obviously, the train hitting a bird will not come to a full stop. In the video, a heavier moving cart collides with an immobile, lighter cart. The momentums of the carts are said to transfer, giving the lighter cart a larger velocity (compared to the original velocity of the heavier cart). But, I'm puzzled as to why the momentum does not completely transfer, i.e. why is any still retained by the heavier cart, considering the lighter cart is moving at a faster velocity than the original cart?

I now realized I may have misread Newton's Principia:

As if the body A impinged upon the body B at rest with 9 parts of motion, and losing 7, proceeded after reflexion with 2, the body B was carried backwards with those 7 parts.

It appears a body can proceed after contact - but, what's important is the fact that the forces are equal and opposite.

I found always, without an error of 3 inches, that when the bodies concurred together directly, equal changes towards the contrary parts were produced in their motions, and, of consequence, that the action and reaction were always equal.

Here's that link again:

http://physics.wfu.edu/demolabs/demos/avimov/mechanics/elastic_collisions/elastic_cars_bs.MPG

 

[Nick O]

Ah, I see. The key thing here is that energy is not transferred instantly. Energy is continually transferred while the objects are in contact. At some point during the energy transfer, enough energy is transferred for the lighter mass to move faster than the heavier mass. At this point, the objects lose contact and energy transfer stops.

It's interesting to note that the lighter mass doesn't accelerate instantly, and the heavier mass doesn't slow down instantly. They compress like springs on a very small scale, and the change in speed propagates through both of the objects at the speed of sound* through the material. This is just Nature's way of avoiding sudden change.

*I think acceleration propagates at the speed of sound, anyway. If not, then the propagation is at least proportional to the speed of sound.

 

[256bits]

The thing is, you can always change your frame of reference.
In the video, it is in relation to a frame where the initial velocity of the second mass is zero, After collision both masses have a forward velocity, albeit the larger mass being slower than before and the smaller mass a larger velocity.

Try it in the frame of reference with the larger mass having zero velocity - ie you are moving forward with the same velocity as the larger mass and see if you can work that out. Difficult to do? Not at all - place the larger mass stationary with respect to you and the table, and have the smaller mass approach with a velocity.

Next, try it from the refererence of the combined centre of mass of both objects - ie each of the masses, the larger and the smaller, each has its own COM, but taken together as a unit, there is a system COM that does not change location, before, during, and after collision. ( Here both masses move towards each other, collide, and move apart )

 

[Lok]

Beside the nice explanations given... You should try the experiment with Gelatin blocks or similar soft materials.
You can observe a compression upon first contact, then tension builds up like in a spring until the lighter cart has been accelerated to the speed of the heavier, and finally the tension is released (has no more inertial opposition) and the lighter object is propelled forward.
This should be the case for most solids, although for most it will be too fast to observe.