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?
The formula of kinetic energy is 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.
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
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 .
Question: In a situation in which data are known to three significant digits, we write . When a number ends in 5 , we arbitrarily choose to write . We could equally well write, “rounding down” instead of “rounding up,” because we would change the number 6.375 by equal increments in both cases. Now consider an order of-magnitude estimate, in which factors of change rather than increments are important. We write because 500 differs from 100 by a factor of 5 while it differs from 1000 by only a factor of 2. We write and What distance differs from 100 m and from 1000 mby equal factors so that we could equally well choose to represent its order of magnitude as, or as , ?
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