A small ball of mass m is initially moving in a circle with a constant speed. The radius of
the circle is n1, and its speed is v0 as shown in the figure. The string
holding the ball passes through a pipe. Now the string is pulled through the pipe which
shortens the radius of the motion. The string is pulled until the radius is n2.
The motion is still circular, but with a faster speed. How much has the kinetic
energy of the ball increased due to pulling the string? If the increase in kinetic energy
is K.E.(final)-K.E.(initial) = Δ K.E. = n3 mv02/2,
what is n3. Note that n1 and n2 have the same units of distance, and
n3 is unitless.
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