Department of Energy Argonne National Laboratory Office of Science NEWTON's Homepage NEWTON's Homepage
NEWTON, Ask A Scientist!
NEWTON Home Page NEWTON Teachers Visit Our Archives Ask A Question How To Ask A Question Question of the Week Our Expert Scientists Volunteer at NEWTON! Frequently Asked Questions Referencing NEWTON About NEWTON About Ask A Scientist Education At Argonne Asymmetrical Newton's Cradle
Name: John M.
Status: N/A
Age: 20s
Location: N/A
Country: N/A
Date: 2001-2002


Question:
When you are dealing with Newton's cradle, say you have 4 balls of equal mass and you pull back balls 1 and 2. Balls 3 and 4 will both go at the same velocity sticking to each other and traveling away from the center. But, if you make the mass of ball 1 = 2x and the mass of the rest of the balls equal x, why do balls 2, 3, and 4 each go at a different velocity? Does it have anything to do with the larger ball (ball 1) having only one pivot point while in the original example, balls 1 and 2 had different pivot points? I would greatly appreciate any input on this question. Thank you.


Replies:
John,

I can see where you would expect to get two balls going out at half the initial speed. In a perfect situation, it would provide conservation of momentum and kinetic energy. I can think of two things that can cause irregularities. One is that the first ball is not EXACTLY two masses. Being off by a few percent could cause problems. A much more likely problem is position. If the centers of mass of all balls involved do not line up perfectly, you can get quite unusual patterns. When all balls are identical, lining them up is fairly easy. If one ball is twice as massive, it is usually bigger. This makes judging a line-up much more difficult. I cannot think of any way around the line-up barrier, if that's what is wrong. Some would try using hollow balls for the lighter ones. The problem this causes relates to resonance. A hollow ball can hold much more energy in its vibrations. This can remove some kinetic energy from the collision. If you can get two different metals, one almost twice as dense as the other, you might have a system with fewer possible defects.

Dr. Ken Mellendorf
Physics Instructor
Illinois Central College


The simplest and most straightforward answer is that the balls move so as to conserve kinetic energy and momentum. With two balls in and two out, this is obviously satisfied. Now if you double the mass of the first ball, for the three balls to move together with the same momentum as the initial ball (2mv), they would have to have velocity 2/3*v. But to have the same kinetic energy, they would have to have velocity square root of 2/3*v. Clearly they cannot have two different velocities and so they move at different velocities.

You might try to calculate what other velocities the three balls could have and still conserve energy and momentum. One obvious solution is the two outer balls move off at the same speed as the incident ball. Together they have the same mass as the incident ball and so with the same velocity they must have the same energy and momentum.

But your experiment shows that the three balls move at different speeds. With three balls, you have an infinite number of solutions. Why your particular one is chosen by the balls then must depend on the details of the collisions and is a difficult problem.

Incidentally, notice that putting a little putty (or chewing gum) between two balls changes the motion drastically. That's because kinetic energy is no longer conserved as some of the energy goes into heating up the putty.

Dick Plano



Click here to return to the Physics Archives

NEWTON is an electronic community for Science, Math, and Computer Science K-12 Educators, sponsored and operated by Argonne National Laboratory's Educational Programs, Andrew Skipor, Ph.D., Head of Educational Programs.

For assistance with NEWTON contact a System Operator (help@newton.dep.anl.gov), or at Argonne's Educational Programs

NEWTON AND ASK A SCIENTIST
Educational Programs
Building 360
9700 S. Cass Ave.
Argonne, Illinois
60439-4845, USA
Update: June 2012
Weclome To Newton

Argonne National Laboratory