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Expert-verified Found in: Page 15 ### Physics For Scientists & Engineers

Book edition 9th Edition
Author(s) Raymond A. Serway, John W. Jewett
Pages 1624 pages
ISBN 9781133947271 # 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${\mathbit{K}}{\mathbf{=}}\frac{{\mathbf{p}}^{\mathbf{2}}}{\mathbf{2}\mathbf{m}}$(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?

1. The unit of momentum is $p=\frac{kg.m}{s}$ .
2. The unit of momentum in terms of N is N.s .
See the step by step solution

## Step 1: Analysis of given data

The formula of kinetic energy is $K=\frac{{\mathrm{p}}^{2}}{2\mathrm{m}}$ 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.

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

Rearrange the above equation for p :

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

Replace kg.m2/s2 for K and kg for m .

$\begin{array}{rcl}p& =& \sqrt{\frac{kg.{m}^{2}}{{s}^{2}}×kg}\\ & =& \sqrt{\frac{{\left(kg\right)}^{2}{m}^{2}}{{s}^{2}}}\\ & =& \frac{kg.m}{s}\end{array}$

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

## 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 .

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

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 . ### Want to see more solutions like these? 