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Explanation of Newton's Cradle by Ron Kurtus - Succeed in Understanding Physics. Also refer to physical science, Isaac Newton, Simon Prebble, Conservation of Momentum and Energy, mass, velocity, friction, inertia, pendulum, Ron Kurtus, School for Champions. Copyright © Restrictions
Newton's Cradle
by Ron Kurtus (revised 19 October 2011)
Newton's Cradle is a clever device that uses a series of equal pendulums to demonstrate the Laws of Conservation of Momentum and Conservation of Energy.
By pulling an end ball away from the others and releasing it, the ball will swing and strike the next ball, causing in the last ball in the series to move away from the group. When the last ball returns, its collision then causes the first ball to move away. This process repeats until it finally wears down. Pulling away several balls will result in the same number of balls moving away at the other end.
This device is often used for demonstrations in the classroom, as well as a toy to amuse people. Newton's Cradle was invented in 1967 by English actor Simon Prebble and named in honor of scientist and mathematician Isaac Newton, because it employs Newton's Laws.
Questions you may have include:
- What is a description of Newton's Cradle?
- What does Newton's Cradle look like in action?
- Why does it work?
This lesson will answer those questions. There is a mini-quiz near the end of the lesson.
Useful tools: Metric-English Conversion | Scientific Calculator.
Description of Newton's Cradle
Newton's Cradle consists of several metal balls (usually 5) suspended from a rack by wires or rods, such that they line up and are almost in contact when in a resting position. There are two wires attached to each ball to keep the pendulum motion in one plane.
Pull up one ball
When an end ball (ball #1) is pulled up and let go, it swings down as a pendulum and hits the next ball. The energy and momentum from that ball is transmitted through the three balls at rest to the ball on the other end (ball #5). That ball is propelled forward at the same speed as the first ball had due to the force of the first collision.
This process continues as ball #5 reaches its peak and then swings down to hit the balls at rest, propelling ball #1 forward and upward.
One ball raised and ready to swing
Note: Although the balls look like they are touching, they are really slightly apart (less than the width of a human hair)
Two or more balls
If two or more balls are pulled up and let go, the collision will result in the same number of balls will be propelled forward on the other end.
Slowly slows down
The action will go back and forth until it slowly slows down due to losses from friction and the elasticity of the balls.
Steel balls are usually used, because they deform very little upon collision and are highly elastic, meaning only a small amount of enegy is lost in the collision.
Simulation
The following simulation allows you to explore Newton's Cradle on your computer, similar to using the real device. (Note that you must have the Flash player installed in your computer to use this simulation.)
Drag on one ball
Place you mouse pointer on an end ball, hold down the left mouse button, and drag the ball, so it is at an angle. Then release the mouse button and let the ball swing free. You will see that only one ball on the other end of the group swings up at about the same speed as the ball you let go.
(Flash animation designed by Bryan Heisey)
Notice that the balls start to slow down and will bounce less and less until they finally stop. This is due to losses from friction and energy that is absorbed in the balls. The effect is called damping of the periodic motion.
Drag multiple balls
You can drag two, three or four balls and let them go. The same number of balls you release will be moved forward upon the collision with the moving balls. This verifies the Law of the Conservation of Momentum, which states that the momentum (mass times velocity) remains the same after a collision.
Explanation and equations
The Law of the Conservation of Energy states that the total kinetic energy of a system with no external forces acting on it remains constant. That means that the kinetic energy of the moving ball or balls upon impact equals the kinetic energy of the balls leaving the other side of the row of balls. At those times, the force of gravity is not a factor.
mv2/2 = MV2/2
where
- m is the mass of the balls being released
- v is the velocity on impact
- M is the mass of the balls moved on the other end
- V is the velocity of the second group of balls after impact
The Law of Conservation of Momentum states that the total linear momentum of a closed system is constant. That means that the momentum of the balls on impact equals the momentum of the second group of balls after impact:
mv = MV
Solving for v and squaring both sides:
v = MV/m
v2 = M2V2/m2
Substituting in the energy equation:
mv2/2 = M2V2/2m = MV2/2
Thus:
M/m = 1 or M = m
This means the mass of the balls leaving equals the incoming mass. Since the balls are of equal mass, that means the same number of balls leave the series as those which impacted the group of balls.
Also, from the equation: V = v
When a ball is pulled outward to some height (h) and let go, gravity causes the ball to swing down as a pendulum. When the ball reaches the bottom of its swing and strikes the next ball, it is traveling at a velocity of approximately:
v = √(2gh)
where
- g is the acceleration due to gravity
- h is the height from which the ball was let go
- √(2gh) is the square root of the product of 2*g*h
The kinetic energy of the moving ball is KE = mv²/2 and its momentum is p = mv, where m is its mass.
Assuming the balls are exactly the same mass, are perfectly elastic and strike along the same axis, the kinetic energy of the moving ball is KE = mv²/2 and the momentum is p = mv, where m is the mass of each ball.
Because the momentum and energy must be maintained in this system, the second ball will move at the same velocity.
Now when two balls are dropped at the same time, the system acts as if the mass has been doubled.
and total mass as the balls that were in initial motion. Thus, if two balls are let go, two balls will be sent in motion after the collision.
Of course, friction and losses due to elasticity will slowly reduce the speed of the balls.
(See Derivation of Principles of Newton's Cradle for an explanation.)
Summary
Newton's Cradle demonstrates laws of motion, including the Laws of Conservation of Momentum and Energy. The simulation allows you to experiment swinging different number of balls to verify the conservation of momentum.
Once you work toward a goal, your inertia moves you toward success
Resources and references
The following resources provide information on this subject:
Websites
Newton's Cradle - by Donald Simanek, Lock Haven University
Conservation of Momentum - Mathematical explanation from the University of Winnipeg, Canada
Books
Top-rated
books on Laws of Motion
Mini-quiz to check your understanding
If you got all three correct, you are on your way to becoming a Champion in Physics. If you had problems, you had better look over the material again.
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