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(a) Calculate $\gamma$ for a proton that has a momentum of 1.00 $\mathrm{kg} \cdot \mathrm{m} / \mathrm{s}$ . (b) What is its speed? Such protons form a rare component of cosmic radiation with uncertain origins.

(a) $1.996 \times 10^{18},(\mathrm{b}) \approx 3.00 \times 10^{8}$

Physics 103

Chapter 28

Special Relativity

Relativity

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Let's sold part, eh? The momentum of the particle be is equal to 1.0 kilogram made her per second, and Moss M is equal to 1.67 Multiply by 10 to the dollar, minus 27 minus 27 kilogram. And if the speed of light C is equal to 3.0 multiply by 10 to the power eat leader per second. Uh, then relent. Mystic factor is given by your ladder. Mystic factor is given by square root off one less be square, divided by M squared times C Square. Let's plug in the Values Square wrote off one less peace creator. Well, momentum is one point ah 00 kilogram o meter per second square, divided by M Square, where losses 1.67 multiplied by 10 to the dollar minus 27. And then we have speed off light a 3.0 multiplied by 10 to the power Eat. Also there all right and simplifying this. Their latest ick factor is equal to one point mine mine. Six Multiply by 10 to the power 18 18 So they're logistic. Factor for Proton logistic factor for raton is equal to 1.996 multiplied by 10 to the power 18. Now let's do part B. Well, they're led a mystic factories keeping by one divided by square root off one minus. We squared, divided by C square. No stalling for we. We is equal to the square root off C square into one minus one. Divided by gonna square and substituting the values we is equal to, uh, squared Rudolph well C square into one minus one, divided by one point mine mine six multiplied by 10 to the power 18 and there is square as well and therefore we is approximately equal to 3.0 multiplied by 10 to the power each meter for a second.

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