# Kinetic energy of N solid bodies

Gold Member

## Main Question or Discussion Point

This is a fairly simple question so I wasn't sure if it belongs here, but it is not a homework question. Just a question on something I'm reading.

The book says there are N solid bodies with initial speed vi (i=1, 2, 3, ..., N)
and final speed vi' after some shock to the system.

The book then says that the difference in kinetic energy is:
$$\sum_{i=1}^{N}m_{i}(v_{i}'^{2}-v_{i}^{2})$$

But my question is, where did the (1/2) factor go from the kinetic energy?

I was even wondering if this has something to do with combining the sum for initial and final kinetic energies into a single script, but if I write the sum out using "j" for initial and "i" for final in the sums it comes out to be what they have but with a (1/2)... like I think it should.
Am I supposed to assume that this is just a typo? Even though several calculations are performed from that equation following its appearance.
I can't see any reason why it would be missing.

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tiny-tim
Homework Helper
Hi Oddbio! But my question is, where did the (1/2) factor go from the kinetic energy?

Am I supposed to assume that this is just a typo? Even though several calculations are performed from that equation following its appearance.
I can't see any reason why it would be missing.
Typo (or laziness of the author)! I assume that it makes no difference to the calculations because it's missing from both sides of every equation.

But the author still shouldn't leave it out without warning. 