Book edition 10th Edition

Author(s) David Halliday

Pages 1328 pages

ISBN 9781118230718

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Short Answer

A spaceship whose rest length is 350 m has a speed of 0.82c with respect to a certain reference frame. A micrometeorite, also with a speed of 0.82c in this frame, passes the spaceship on an antiparallel track. How long does it take this object to pass the ship as measured on the ship?

The time taken by the object to pass the ship is $1.2 μs$ .

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Describe the expression for the velocity of the particle

Suppose a particle is moving with speed u^' in x^' in an inertial frame S^'. If the frame S^' is moving with a velocity v with respect to another frame S, then the velocity of the particle with respect to frame S is given by,

$u = \frac{u^{'} + v}{1 + \frac{u^{'} v}{c^{2}}}$ .....................(1)

Here, the speed of the light is c.

Step 2: Determine the time taken by the object to pass the ship

Rearrange the equation (1) for u^'.

$\begin{array}{rcl} u (1 + \frac{u' v}{c^{2}}) & = & u^{'} + v \\ \frac{{uu}^{'} v}{c^{2}} - u^{'} & = & v - u \\ u' (\frac{uv}{c^{2}} - 1) & = & v - u \\ u^{'} & = & \frac{v - u}{(\frac{uv}{c^{2}} - 1)} \end{array}$

Substitute 0.82c for u, and -0.82c for v in equation (2).

$u^{'} = \frac{- 0.82 c - 0.82 c}{\frac{(- 0.82 c) (0.82 c)}{c^{2}} - 1} u^{'} = 0.98 c$

The expression to calculate the time is given by,

data-custom-editor="chemistry" $∆ t^{'} = \frac{∆ x}{u^{'}}$

Substitute 350m for data-custom-editor="chemistry" $∆ x$ and 0.98c for u^' in equation (3).

$\begin{array}{rcl} ∆ t^{'} & = & \frac{350 m}{0.98 c} \\ = & \frac{350 m}{0.98 (3 \times 10^{8} m / s)} \\ = & 1.2 \times 10^{- 6} s \\ = & 1.2 μs \end{array}$

Therefore, the time taken by the object to pass the ship is data-custom-editor="chemistry" $1.2 μs$ .

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Fundamentals Of Physics

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Short Answer

A spaceship whose rest length is 350 m has a speed of 0.82c with respect to a certain reference frame. A micrometeorite, also with a speed of 0.82c in this frame, passes the spaceship on an antiparallel track. How long does it take this object to pass the ship as measured on the ship?

Step by Step Solution

Step 1: Describe the expression for the velocity of the particle

Step 2: Determine the time taken by the object to pass the ship

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Fundamentals Of Physics

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Short Answer

A spaceship whose rest length is 350 m has a speed of 0.82c with respect to a certain reference frame. A micrometeorite, also with a speed of 0.82c in this frame, passes the spaceship on an antiparallel track. How long does it take this object to pass the ship as measured on the ship?

Step by Step Solution

Step 1: Describe the expression for the velocity of the particle

Step 2: Determine the time taken by the object to pass the ship

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