Asymmetrical Newton's Cradle
Name: Elizabeth H.
I am currently conducting a experiment of Newton's Cradle
with nine plastic spheres. Each of the spheres is slightly smaller in
diameter, and therefore mass, than the one before it. What are the
equations I need to find the transfer of the energy if ball 1 is dropped
and released with a velocity of x?
You need equations that set the total energy and momentum before ball
1 collides with the others equal to the total energy and momentum after
the collision. (In general you would also have to consider conserving
angular momentum, but if all masses are suspended from the same height,
angular momentum conservation will not tell you anything that linear
momentum conservation did not already tell you.)
Total momentum = m1*x
Total energy = m1*x*x/2
Total momentum = m1*v1 + m2*v2 + m3*v3 ...
Total energy = m1*v1*v1/2 + m2*v2*v2/2 + m3*v3*v3/2 ...
You also have to have equations (inequalities, actually) to reject
any solutions of the energy- and momentum-conservation equations that
would require masses to move through each other.
v1 <= v2 <= v3 <= v4 <= v5 <= v6 <= v7 <= v8 <= v9
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Update: June 2012