28.5 Relativistic Momentum

In Relativistic Energy, the relationship of relativistic momentum to energy is explored. That subject will produce our first inkling that objects without mass may also have momentum.

What is the momentum of an electron traveling at a speed $0 . \text{985} c$? The rest mass of the electron is $9 . \text{11} \times \text{10}^{- \text{31}} \text{ kg}$.

Find the momentum of a helium nucleus having a mass of $6 . \text{68} \times \text{10}^{–\text{27}} \text{ kg}$ that is moving at $0 . \text{200} c$.

(a) Find the momentum of a $1 . \text{00} \times \text{10}^{9} \text{ kg}$ asteroid heading towards the Earth at $\text{30}.\text{0 km}/\text{s}$. (b) Find the ratio of this momentum to the classical momentum. (Hint: Use the approximation that $\gamma = 1 + \left(\right. 1 / 2 \left.\right) v^{2} / c^{2}$ at low velocities.)

What is the velocity of an electron that has a momentum of $3.04 \times \text{10}^{–\text{21}} \text{ kg}\cdot\text{m}/\text{s}$? Note that you must calculate the velocity to at least four digits to see the difference from $c$.

(a) Calculate the speed of a $1.00- \mu \text{g}$ particle of dust that has the same momentum as a proton moving at $0 . \text{999} c$. (b) What does the small speed tell us about the mass of a proton compared to even a tiny amount of macroscopic matter?