A 1.0 g particle has momentum 4 x 105 kg m/s. What is the particle's speed in m/s? What is thisparticle's rest energy, kinetic energy, and the total energy?

Answered: A 1.0 g particle has momentum 4 x 105…

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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A 1.0 g particle has momentum 4 x 105 kg m/s. What is the particle's speed in m/s? What is this
particle's rest energy, kinetic energy, and the total energy?

Expert Solution

Step 1

The expression for momentum, P is $P = m v$ . Here $m$ and $v$ are the mass and velocity respectively.

Substitute for mass and momentum in the above equation and obtain the velocity.

$\begin{array}{rcl} P & = & \frac{m v}{\sqrt{1 - \frac{v^{2}}{c^{2}}}} \\ v & = & \sqrt{\frac{p^{2} c^{2}}{m^{2} c^{2} + p^{2}}} \\ = & \frac{(4 \times 10^{5} k g m / s) (3 \times 10^{8} m / s)}{\sqrt{{(1 \times 10^{- 3} k g)}^{2} {(3 \times 10^{8} m / s)}^{2} + {(4 \times 10^{5} k g m / s)}^{2}}} \\ = & 2.4 \times 10^{8} m / s \end{array}$

Hence the speed of the particle is $2.4 \times 10^{8} m / s .$

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