# Ball bearings momentum physics problem

Gold Member
Two ballbearings are attached to strings of length 3.6m. The mass of ballbearing A is 1.6kg, and B is 1.2kg. Plasticine is attached to each ballbearing, so that they stick together on collision.

The strings are attached to the same place on a roof, so that the ball bearings are hanging next to eachother. Ballbearing A is raised so that its string makes an angle of 50 degrees to the vertical, and then released.

What is the combined velocity of the balls just after they have collided, and what vertical height do they reach?

When the balls are at their maximum height after the collision, their velocity is momentarily zero. Where has the momentum gone?

To find the combined velocity, i just use trigonometry to find the vertical height the balls are raised by (~1.286m). I then used the fact that total mechanical enegery is conserved to find the velocity of A just before it strikes B. Then, using conservation of momentum, i found the combined velocity to be 2.9 m/s.

For the maximum height after the collision, i just used the same idea. I calculated the total mechanical energy just after the collision, using the combined velocity. I then found what height this corresponds to (in terms of gravitational potential energy), since kinetic energy will be zero at the highest point. I got an answer of 0.42m.

Now, both of these answers are correct according to my book, but it doesnt give an answer for the final question, and im not too sure about it. I realise that momentum is conserved, so it cant have just dissappeared. My thought was that it is transferred to the string, but im not very sure about this.

Any help would be appreciated,
Thanks,
Dan.

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according to what you have written above, your working is correct, as i also obtain the same answers of you. The last answer inclusive.

what exactly is the physics test on?

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danago,

Are you sure the momentum is conserved?
Why should it be conserved?
When is momentum conserved?
I momentum always conserved?

Michel

Gold Member
Well unless my textbook and teacher have been lying to me, yes, im sure momentum is conserved, although, it is not necessarily maintained within an isolated system, due to air resistance etc.

yes danago, the textbook AND teacher are BAD PHYSICS, there lying! (points)

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I'm curious I thought momentum was always conserved, energy not, depending....This is really fundamantal. Why would anyone suggest that momentum should not be conserved within an inertial frame of reference?

danago,
denverdoc,

When externals forces are acting on a system, the momentum is not conserved.
However, energy might still be conserved, if these forces are conservative (!).
In this case, kinetic energy might be transformed in potential energy and the momentum might change.

However, if you consider objects in the gravity field of the earth, you can see things from two different point of view.

First, these objects are in an external force field: then the total momentum of these objects will not be conserved as the gravity field may work on these objects to change their total momentum.

Second, if you consider these objects and the earth together as one system, then the total momentum should be conserved since the gravity will be an internal (and conservative) force within this larger system. In this case, when the objects have lost their momentum, the earth must have gained this momentum. It is clear that when the momentum of small objects on the earth are "transfered" to the earth, this does not have a big IMPACT on the earth. However, it has been said that during this last big tsunami, the earth has been really shaked a little bit on its orbit by the initial earthquake, just as a consequence of momentum conservation (although the conservation should not be perfect in this case because of many possible way of dissipating is, like by losing energy in the waves)

Michel

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danago,
denverdoc,

When externals forces are acting on a system, the momentum is not conserved.
However, energy might still be conserved, if these forces are conservative (!).
In this case, kinetic energy might be transformed in potential energy and the momentum might change.

However, if you consider objects in the gravity field of the earth, you can see things from two different point of view.

First, these objects are in an external force field: then the total momentum of these objects will not be conserved as the gravity field may work on these objects to change their total momentum.

Second, if you consider these objects and the earth together as one system, then the total momentum should be conserved since the gravity will be an internal (and conservative) force within this larger system. In this case, when the objects have lost their momentum, the earth must have gained this momentum. It is clear that when the momentum of small objects on the earth are "transfered" to the earth, this does not have a big IMPACT on the earth. However, it has been said that during this last big tsunami, the earth has been really shaked a little bit on its orbit by the initial earthquake, just as a consequence of momentum conservation (although the conservation should not be perfect in this case because of many possible way of dissipating is, like by losing energy in the waves)

Michel

Nice answer. I was thinking in only term of collisions.

The simplest way to look at it mathematically is
$$\frac{dp}{dt}=F$$
If the force along a direction is 0, the momentum change is 0, ie., the momentum is conserved. Note that it is only along THAT direction in which the momentum is conserved.