Your explanation does not answer the fundamental question I have had about Newton's Cradle for many years. Here is my question and my thoughts on the matter:
The Click-Clack Toy - I call it that for want of a better name.
Five chrome steel balls (like the balls from a large ball bearing) about 20 mm in diameter are suspended in a row from a wooden frame. At rest the balls just touch one another. The suspending cords pass through the diameters of the balls, then angle upward, at about a 45 degree angle, to the wooden frame.
If you take hold of one of the end balls, say the one to your left, swing it outward, keeping the suspending cords taut, and let it go. It swings inward, strikes the second ball and immediately the right hand ball, the 5th ball, swings out. The three balls in the center do not move.
The right hand ball, the 5th ball, when it reaches the end of its arc travels back, hits the 4th ball and the 1st ball immediately swings outward. Again the three balls it the center do not move. This continues until the original energy is dissipated. The toy makes a click-clack sound as a ball hits one another ball, thus my name for this device.
So far this seems reasonable enough. But when you raise two balls on the left, balls 1 and 2, holding the 2nd ball and release them when 1 and 2 strike the 3rd ball balls 4 and 5 move out together. The action continues, the 3rd ball remaining stationery in the center.
If you raise the first three balls and release them upon impact the 3rd ball moves away along with the 4th and 5th balls. 1 and 2 remain in place, 3, 4, and 5 return and strike the 2nd ball and 1, 2, and 3 move to the left, leaving 4 and 5 in place, and so forth.
If you raise the first four balls when the 4th ball strikes the 5th ball, balls 2, 3, 4, continue to move to the right with the 5th ball leading the train and the 1st ball stops and stands still. When balls 2, 3, 4 and 5 return to strike the 1st ball the 5th ball remains stationery and balls 1 ,2, 3, and 4 move to the left, and so forth.
Why does it work this way? That question has intrigued me for years.
Considering the one ball case, it seems obvious to me that the energy that propels the 5th ball outward travels as a compression wave through the 2nd, 3rd and 4th balls. I further believe that the 5th ball moves when this compression wave is reflected by the right hand side of the 5th ball. Otherwise how does the 5th ball know that there is not a 6th ball beyond it? I am saying it is not the 4th ball striking the 5th ball that moves the 5th ball, it is the reflected shock wave.
This could be tested with hard steel shafts of differing lengths suspended with two strings. Strike one end and measure the time until the rod moves. I am suggesting the rod only moves when the compression wave is reflected at the far end. Thus a longer rod would take a longer time before it moves.
Ok, that is out of the way,
Now consider the two ball case. The 4th and 5th balls move out together. But the shock wave has already traveled through the 4th ball, and how does it know there is not a 6th ball out there, if there is a 6th ball the 5th and 6th balls would swing out together. And any energy that would move the 4th ball has already passed through the 4th ball. So it seems the 5th ball should move out with twice the energy, leaving balls 1 through 4 behind. So my theory about reflected compression waves seems to break down.
Could it be that when you raise and drop the 1st and 2nd ball two shock waves travel down the line of balls. The leading shock wave generated when 2 hits 3, the following shock wave generated when 1 "hits" 2. The problem is that 1 and 2 are touching already. But two shock waves would explain how 4 and 5 move out, each one moving when its shock wave is reflected from its far side.
I welcome your thoughts on this matter.
It would be interesting to take a high speed video of the click-clack in action. Then the exact times of the balls' motions could be determined, and compared to the speed of sound in steel.
Well made click-clacks used to be sold by Sharper Image stores (since closed down), for appreciably more than $50. The ran for quite a long time. I have also seen cheaper versions, with smaller balls and less precise construction. They would only run for a few minutes
Del
Currently living on a tropical island west of the Republic of Panama
Del - USA
18045
Answer
You go into quite a thorough analysis of what happens to the balls in a Newton's Cradle device. Thanks for your observations.
The principle is simply a combination of the Conservation of Momentum and Energy.
Let each ball has mass "m" and the initial balls move at velocity "v". Suppose you swung two balls. Thus, for momentum 2mv = MV, where M is the total mass moved on the other end and V is its velocity. For energy, E = 2mv^2/2 = MV^2/2. Solving the momentum equation for m and substituting into the energy equation, you get the resulting velocity V = v. Solving the momentum equation for v, squaring it and substituting into the energy equation, you get the resulting mass M = 2m. In other words, if you swing two balls, the result will be two balls at the same velocity. This hold for any number of balls you swing.
In the real world, the balls are somewhat elastic, such that energy is lost in the collisions. Also, the transfer of energy and momentum is not perfect, and could be described by your "shock wave".
The less losses to misalignment, elasticity, and other factors can make the cradle click back-and-forth a much longer time.
what are the energy changes taking place in the system?
- USA
17722
Answer
In a perfect system, all of the kinetic energy of a moving ball is transferred into the ball that it strikes. But in the real world, some of the kinetic energy is lost to heat and another small part is not transferred because of the elasticity of the balls.
what are the basic energy changes taking place in the system?based on the diagram u on the website, would you say that ball 1's momentum equal ball's 5 momentum, ie, m1v1 = m2v2 = m4v4 = m5v5?
- USA
17715
Answer
The momentum of the first ball is transferred to the second, which then transfers the momentum to the third ball, and so on to the end ball.
The Law of Conservation of Momentum states that the total momentum of the system remains constant. Likewise, the energy is transferred from one ball to another, such that the total energy remains constant.
based on the newton's cradle, what happens to the momentum fo the first ball and what happens to the momentum gained by the second ball? also, what has occurred in terms of forces?
- USA
17711
Answer
The momentum and energy of the first ball provides a force on the second ball. Since they have the same mass and due to the laws of the Conservation of Momentum and Conservation of Energy, the momentum and energy is transferred to the second ball. This transfer continues until the last ball, which moves up freely.
What is the the longest time the cradle has run for?
Jessica - UK
16672
Answer
The length of time the a Newton's cradle will run depends on the amount of friction in the strings, the length of the stings, the alignment of the balls and how hard the balls are.
The ones you can buy in the store bounce back and forth much less than a minute.
How does Newton's Cradle demonstrate Newton's second law?
- USA
15515
Answer
When the moving ball strikes the stationary ball, it applies a force on that ball, thus accelerating it into motion. The first ball decelerates and stops moving.
Since F = ma, if two balls are moving and hit the stationary ball, then two balls will accelerate.
if i drop 2 balls will the height of the reacting ball be higher than if if i just drop one ball
thanks
jonas - USA
15135
Answer
If you drop one ball, then one ball should go up to the height of the first ball. If you drop two balls, then two balls should go up to the same height those two balls dropped from. This is due to the Conservation of Energy and of Momentum.
But note that due to losses from friction, the second ball(s) will go up slightly less than the initial ball(s).
i love your site you guys are so helpful i am making a newtons cadle in my woodshop class i have already figured out my lenghts and i am going to us golf balls i was wondering if i make the legs square if it would have any affect on the cradle of if they have to be round?
Jeanne - USA
14959
Answer
You want to have a nice structure that would hold the balls and their strings, in order that the balls would line up and swing freely. The shape of the legs do not matter. The main thing is that they don't get in the way. But also, you want to make them thin enough to be able to see the balls in motion.
Did you do the flash animation of Newton's cradle on your "School for Champions" website? It is the best and most functional simulation of the "ideal" behavior of Newton's Cradle that I've seen. I have a web document on this subject, and would like permission to use your animation, with credit to its creator of course. If this is ok, please specify exactly how you want it credited.
-- Donald Simanek, Emeritus Professor of Physics, Lock Haven University of Pennsylvania.
- USA
14917
Answer
Bryan Heisey, a Flash developer, created the Newton's Cradle simulation. It certainly is a well-done simulation. He submitted it to Flashkit.com as a free, downloadble demonstration. I adjusted the code a little for use in our site.
Heisey's website is at http://www.bryanheisey.com/base_content.html
You certainly have permission to use the animation. Besides giving Heisey credit, I'd appreciate reference to our website also.
i am making a newtons cradle and i was wondering what the best type of wood would be for the stand also what size is the best i had one that i measred buti was wondering if i could make it bigger and does the size of the balls contribute to how big the frame is? thanks Jeanne
Jeanne - USA
14731
Answer
The type of wood for the stand doesn't matter, but heavier wood is better to keep the device more stable.
The size of the Newton's Cradle depends on the size of the balls you intend to use. You want to make something that is not too small that it is hard to make and not too big that it would take too much material. Draw a picture of what you want to make approximately the size that would be the most convenient.
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