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Newton's Cradle is a clever device that
not only demonstrates a pendulum, but also shows the Law
of Conservation of Momentum and Energy. Friction and
damping effects are also observed. This device is often
used as a toy to amuse people. Newton's Cradle was
invented in the late 1600s by scientist and
mathematician Isaac Newton. Some
questions you may have are:
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What is Newton's Cradle?
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What does it look like?
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Why does it work?
This lesson will answer those questions.
There is a mini-quiz near the end of the lesson.
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 in
contact when in a resting position. There are two wires
attached to each ball to keep the pendulum motion in one
plane.
When an end ball 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. That ball is
propelled forward at the same speed as the first ball
had due to the force of the first collision.
If two or more balls are pulled up and let go, the same
number of balls will be propelled forward due to the
collision.
Since it is a form of pendulum, the action will go back
and forth until it slowly slows down due to losses from
friction and the elasticity of the balls.
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 Macromedia Flash player installed in your
computer to use this simulation.) 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.
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.
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 When one or
more balls are pulled up and let go, they swing down as
a pendulum. The velocity (v) of the balls, when they hit
the resting balls is determined by the height (h) from
where they were let go and the acceleration of gravity
(g). The velocity is approximately v = SQRT(2*h/g).
The kinetic energy of the balls is KE = m*v2/2 and the
momentum is p = m*v, where m is the mass of the balls in
motion. Because the momentum and energy
must be maintained in this system, the balls that move
will have the same velocity 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. In conclusion
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. |
