## College Physics (4th Edition)

The relativistic momentum is $8.0000000029\times 10^8~kg~m/s$ The non-relativistic momentum is $8\times 10^8~kg~m/s$ The percentage difference is $0.000000036\%$
We can find the value of $\gamma$: $\gamma = \frac{1}{\sqrt{1-\frac{v^2}{c^2}}}$ $\gamma = \frac{1}{\sqrt{1-\frac{(8\times 10^3~m/s)^2}{(3.0\times 10^8~m/s)^2}}}$ $\gamma = 1.00000000036$ We can find the relativistic momentum: $p_{rel} = \gamma ~m~v$ $p_{rel} = (1.00000000036)(1\times 10^5~kg)(8\times 10^3~m/s)$ $p_{rel} = 8.0000000029\times 10^8~kg~m/s$ The relativistic momentum is $8.0000000029\times 10^8~kg~m/s$ We can find the non-relativistic momentum: $p = m~v$ $p = (1\times 10^5~kg)(8\times 10^3~m/s)$ $p = 8\times 10^8~kg~m/s$ The non-relativistic momentum is $8\times 10^8~kg~m/s$ We can find the percentage difference: $\frac{(8.0000000029\times 10^8~kg~m/s)-(8\times 10^8~kg~m/s)}{8\times 10^8~kg~m/s}\times 100\% = 0.000000036\%$
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