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Name: Elizabeth H.
Status: student
Age: 16
Location: N/A
Country: N/A
Date: 2001-2002

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

Tim Mooney

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