Book edition 9th Edition

Author(s) Raymond A. Serway, John W. Jewett

Pages 1624 pages

ISBN 9781133947271

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Short Answer

Kinetic energy K (Chapter 7) has dimensions kg.m²/s² . It can be written in terms of the momentum p (Chapter 9) and mass m as
$K = \frac{p^{2}}{2 m}$
(a) Determine the proper units for momentum using dimensional analysis.
(b) The unit of force is the newton N, where 1 N = 1 kg.m/s² . What are the units of momentum p in terms of a newton and another fundamental SI unit?

The unit of momentum is $p = \frac{k g . m}{s}$ .
The unit of momentum in terms of N is N.s .

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Analysis of given data

The formula of kinetic energy is $K = \frac{p^{2}}{2 m}$ where K is the kinetic energy, p is the momentum, and m is the momentum.

It has given that:

The dimension of kinetic energy is kg.m²/s² .

The analysis of a relationship between different physical quantities by using the units of measurements and dimensions is called dimensional analysis. It is used to examine the correctness of an equation.

Step 2(a): Determination of units of momentum

Consider the above equation of kinetic energy.

$K = \frac{p^{2}}{2 m}$

Rearrange the above equation for p :

$\begin{array}{rcl} p^{2} & = & 2 K m \\ p & = & \sqrt{2 K m} \end{array}$

Replace kg.m²/s² for K and kg for m .

$\begin{array}{rcl} p & = & \sqrt{\frac{k g . m^{2}}{s^{2}} \times k g} \\ = & \sqrt{\frac{{(k g)}^{2} m^{2}}{s^{2}}} \\ = & \frac{k g . m}{s} \end{array}$

Hence, the unit of momentum is $p = \frac{k g . m}{s}$

Step 3(b): Determination of the units of momentum in terms of Newton

The momentum is given by the product of force in L and some unknown quantity X .

p = N . X

Replace kg.m/s² for N and kg.m/s for p .

$\frac{k g . m}{s} = \frac{k g . m}{s^{2}} . X$

Find the unit for X

X = s

Now, replace s for X to get the units of p in terms of N .

$\begin{array}{rcl} p & = & N . X \\ = & N . s . \end{array}$

Hence, the unit of momentum in terms of N is N.s .

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Physics For Scientists & Engineers

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Short Answer

Step by Step Solution

Step 1: Analysis of given data

Step 2(a): Determination of units of momentum

Step 3(b): Determination of the units of momentum in terms of Newton

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Physics For Scientists & Engineers

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Short Answer

Step by Step Solution

Step 1: Analysis of given data

Step 2(a): Determination of units of momentum

Step 3(b): Determination of the units of momentum in terms of Newton

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