## Physics for Scientists and Engineers: A Strategic Approach with Modern Physics (4th Edition)

(a) $p = 1.12\times 10^{-17}~kg~m/s$ (b) The proton's momentum exceeds its Newtonian momentum by the factor $22.4$
(a) We can find $\gamma$: $\gamma = \frac{1}{\sqrt{1-\frac{v^2}{c^2}}}$ $\gamma = \frac{1}{\sqrt{1-\frac{(0.999~c)^2}{c^2}}}$ $\gamma = \frac{1}{\sqrt{0.001999}}$ $\gamma = 22.4$ We can find the proton's relativistic momentum: $p = \gamma ~m~v$ $p = (22.4)(1.67\times 10^{-27}~kg)(0.999)(3.0\times 10^8~m/s)$ $p = 1.12\times 10^{-17}~kg~m/s$ (b) The proton's momentum exceeds its Newtonian momentum by the factor $\gamma$ Therefore, the proton's momentum exceeds its Newtonian momentum by the factor $22.4$