Answered: A brick of mass 1kg travels to the…

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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Question

A brick of mass 1kg travels to the right at 0.8c, where c is the speed of light. It collides with another brick of mass 2kg which is at rest before the collision. After the collision, the lighter brick has a speed of 0.67c, still to the right.

What is the momentum of the heavier brick after the collision? Keep three significant digits.

(Hint: be careful to use the relativistic expressions for momentum)

Expert Solution

Step 1

Given:

Mass(m₁) = 1 kg

Mass(m₂) = 2 kg

Before collision velocity of m₁(v₁) = 0.8c

Before collision velocity of m₂(v₂) = 0

After collision velocity of m₁(v') = 0.67c

Now,

mass m₁ using relativistic expression

$\Rightarrow m^{'} = \frac{m_{1}}{\sqrt{1 - \frac{v^{2}}{c^{2}}}}$

$\Rightarrow m^{'} = \frac{1}{\sqrt{1 - \frac{{(0.8 c)}^{2}}{c^{2}}}}$

$\Rightarrow m^{'} = 1.67 k g$

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