Using relativistic expressions, compare the momentum of two...

Using relativistic expressions, compare the momentum of two electrons, one moving at $2.00 \cdot 10^{8} \mathrm{~m} / \mathrm{s}$ and the other moving at $2.00 \cdot 10^{3} \mathrm{~m} / \mathrm{s}$. What is the percent difference between nonrelativistic momentum values and these values?

Key Concepts

Lorentz Factor

The Lorentz factor, denoted by ?, quantifies how much time dilation, length contraction, and the increase in mass (or inertia) occur at high velocities. It plays a critical role in converting classical expressions to their relativistic counterparts, illustrating how quantities like momentum deviate from classical predictions as velocity approaches the speed of light.

Percent Difference

Percent difference is a metric used to compare the relative difference between two values. In the context of momentum calculations, it is used to quantify the deviation between the nonrelativistic momentum and the relativistic momentum, highlighting the magnitude of correction needed when high speeds are involved.

Nonrelativistic Momentum

Nonrelativistic momentum is calculated using the classical formula p = mv, which assumes that the speeds involved are much smaller than the speed of light. This approximation is valid when relativistic effects are negligible, but it fails to capture the significant corrections needed at relativistic speeds.

Relativistic Momentum

Relativistic momentum is defined as p = ?mv, where ? (the Lorentz factor) = 1/?(1 - (v/c)²). This expression accounts for the increases in inertia at speeds close to the speed of light, making it necessary when dealing with high-velocity particles, as classical momentum p = mv becomes inaccurate.

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