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Physics For Scientists & Engineers
Found in: Page 15

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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


(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=kg.ms .
  2. The unit of momentum in terms of N is N.s .
See the step by step solution

Step by Step Solution

Step 1: Analysis of given data

The formula of kinetic energy is K=p22m 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.


Rearrange the above equation for p :


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


Hence, the unit of momentum is p=kg.ms

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 .


Find the unit for X

X = s

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


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


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