# Ball bearings momentum physics problem

• danago
In summary: If there is no external force, the momentum is conserved in ALL directions.In summary, the conversation discusses the concept of conservation of momentum and its application to a physics problem involving two ballbearings attached to strings of different lengths and masses, raised and released at an angle and colliding after which their combined velocity and maximum height are calculated using trigonometry and conservation of mechanical energy. The final question raises a discussion on the possibility of momentum being transferred to the string and the concept of conservation of momentum in the presence of external forces.

#### danago

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 each other. 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 doesn't give an answer for the final question, and I am not too sure about it. I realize that momentum is conserved, so it can't have just dissappeared. My thought was that it is transferred to the string, but I am not very sure about this.

Any help would be appreciated,
Thanks,
Dan.

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

Well unless my textbook and teacher have been lying to me, yes, I am 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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lalbatros said:
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.

## 1. How do ball bearings affect momentum in a physics problem?

In a physics problem, ball bearings can affect momentum by either adding to or reducing the overall momentum of an object. This is because ball bearings have mass and velocity, which are two components of momentum. When they collide with an object, they can transfer their momentum to that object, resulting in a change in its overall momentum.

## 2. What is the equation for calculating momentum in a ball bearings problem?

The equation for momentum is p = mv, where p is momentum, m is mass, and v is velocity. In a ball bearings problem, this equation can be used to calculate the momentum of the ball bearings before and after a collision, and to determine the change in momentum of the system.

## 3. How does the mass of the ball bearings affect the momentum in a physics problem?

The mass of the ball bearings plays a crucial role in determining the overall momentum in a physics problem. The greater the mass of the ball bearings, the greater the amount of momentum they possess. This means that in a collision, ball bearings with a larger mass will transfer more momentum to the object they collide with.

## 4. What is the law of conservation of momentum and how does it apply to ball bearings in a physics problem?

The law of conservation of momentum states that in a closed system, the total momentum before and after a collision will remain constant. This means that the total momentum of all objects involved in a ball bearings problem will remain the same, even after a collision. This law can be used to solve for unknown quantities in a physics problem involving ball bearings.

## 5. How can the concept of impulse be applied to a ball bearings momentum physics problem?

Impulse is the change in momentum of an object over a certain period of time. In a ball bearings problem, impulse can be used to calculate the change in momentum of the ball bearings or the object they collide with. This can be useful in determining the force exerted during a collision and the resulting change in momentum of the system.