Project Involving Newton's Cradle

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In summary, the conversation is about analyzing a simple Newton's Cradle in class to supplement learning of impulse and momentum. The project involves determining the amount of time for the apparatus to come to rest using only two masses instead of the typical three or more. The group is considering using the harmonic motion of a simple pendulum with each mass independent of the other to simplify the task. There are currently no knowns and an Excel file has been attached for analysis. The next step is to identify sources of damping and use momentum-impulse relations to analyze the collision. There may be restrictions on what can be measured, leading to complications in using energy relationships. One suggestion is to model a range of scenarios with varying energy loss per collision to determine the
  • #1
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We are analyzing a simple Newton's Cradle in class to supplement our learning of impulse and momentum. Our project requires us to determine the amount of time it takes for the apparatus to come to rest. In our analysis we are to only use two masses, not the typical 3+. My group and I are trying to use the harmonic motion of a simple pendulum with each mass independent of the other. Will this simplify our task or only make it harder? As of now, there are NO knowns. I have attached our excel file. Our next step should be to analyze the collision, but we are not sure how.
 

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  • #2
You need to work out how much energy is lost each time the two balls collide.

You can potentially work that out by observing the height to which the "outgoing" ball rises after being hit by the "incoming" ball, bearing in mind the starting height of the incoming ball.

Does that make sense?

I assume you know about gravitational potential energy.
 
  • #3
It is not clear whether you are including the effects of damping, but if you aren't then you should, because if you don't your model will never reach a state of rest (i.e. the system will keep oscillating forever).

Next step is to identify the sources of damping. Two that spring to mind are;
- Air resistance.
- Inelastic collisions.

Air resistance can probably be neglected in this case.

On the issue of treating the masses independantly - You are trying to determine how long it will be before the system comes to rest. Essentially you are measuring the rate at which the system dissipates energy. Treating the masses seperately, or indeed trying to use forces at all would be taking the difficult path. My suggestion would be to relate energy loss per second to the number of collisions per second, which can in turn be related to the natural frequency of the pendulum.

Essentially you can treat both masses a a single pendulum that periodically loses energy.

As you mentioned, there are no knowns, so there won't be a single definative answer. You should obtain an answer that depends on the initial height of the pendulum the energy lost in each collision (which could be further related to the elasticity of the balls themselves etc depending on how in depth you wished to go), and the natural frequency of the pendulum (which depends on string length).

Claude.
 
  • #4
Thank you for your responses. Mr. James, we do realize that we need to determine energy loss, but there are no tools for measurement in this project. We did consinder energy relationships, but they seemed to only further complicate our problem since we cannot measure the height and angle of the second mass after the collision. Mr. Claude, we have not yet included damping, but that is the are we are trying to solve. Thank you for clarifying my question. We are not treating the masses seperately but rather assuming the two masses to be a single pendulum with the collision being the damping effect. At the moment we are looking at using momentum-impulse relations to analyze the actual collision. We have a relationship between the two velocities and the coefficient of restitution, but we are not sure how to get that back to the harmonic motion in the excel file.
 
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  • #5
We did consinder energy relationships, but they seemed to only further complicate our problem since we cannot measure the height and angle of the second mass after the collision.

Why can't you measure height?

Are there restrictions on what you are allowed to measure? If so, please post them so we can think about this.
 
  • #6
Okay, I took a look at the excel file and I will make some further comments.

Do you think it is fully necessary to model the position, velocity and acceleration of the pendulum? All you are trying to figure out is how long it will take to lose all its energy.

Also, I think there is some confusion between the angular velocity of the pendulum and the angular velocity of its oscillation. The angular velocity will vary, reaching a maximum at the lowest point and zero at the endpoints. The angular velocity of the oscillation will be constant because the period (as I noticed you have calculated) is constant, since g and L are constant. The angular velocity of the oscillation is defined as;

[tex] \omega = \frac{2\pi}{T} [/tex]

It is this quantity that is constant. To avoid confusion, I suggest using v rather than omega to denote the velocity, since by the small angle approximation these two quanities are nearly equal anyway.

Finally, as I mentioned in my previous post, the energy lost per collision does not necessarily have to be known. You could model a range of scenarios where the energy lost per collision varies, coming up with a range of time values. The key is relating the time taken to reach rest (call it [itex] t_r [/itex]) with the energy lost per collision (call it [itex] E_c [/itex]) the initial energy (call it [itex] E_0 [/itex]) and the frequency of the pendulum (call it [itex] \omega [/itex]) so you get something like this;

[tex] t_r = f(E_c,E_0,\omega) [/tex]

Claude.
 
  • #7
In the such case, if you use at least 5 beads or marbles the amount you pull back should show more time unless you use all but 1. In that case, it will act as you pulled only one bead back due to the loss of kinetic energy. If you use an even amount of beads, try to pull back half. I am doing this precise project for a science fair. I will try to record the information I gather. Hope it helps.

Alex Bertrand
 

What is Newton's Cradle and how does it work?

Newton's Cradle is a device that demonstrates the conservation of momentum and energy. It consists of a row of suspended metal balls, usually five in number, that are connected by strings. When one ball is lifted and released, it collides with the next ball, transferring its momentum and causing the last ball to swing out. The last ball then transfers its momentum back to the first ball, causing it to swing out and the cycle repeats.

What is the purpose of a project involving Newton's Cradle?

The purpose of a project involving Newton's Cradle is to demonstrate and visualize the principles of conservation of momentum and energy in a simple and tangible way. It can also be used to explore the concepts of force, motion, and collisions.

What materials are needed to create a Newton's Cradle?

To create a Newton's Cradle, you will need 5 metal balls, preferably of the same size and weight, 5 strings or wires of equal length, and a sturdy frame or support to hang the balls from. You may also need tape or glue to secure the strings to the balls and frame.

What factors affect the movement of a Newton's Cradle?

The movement of a Newton's Cradle is affected by various factors, including the size and weight of the balls, the materials they are made of, the length and tension of the strings, and the angle at which the balls collide. The surface on which the cradle is placed can also affect its movement.

What are some real-world applications of Newton's Cradle?

Although Newton's Cradle is mainly used for educational and entertainment purposes, its principles can be applied in real-world situations. For example, the concept of conservation of momentum is used in car safety features such as airbags and seatbelts. The principles of collision and energy transfer are also relevant in sports such as billiards and bowling.

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