Answer to Question #135383 in Classical Mechanics for Sofia rose

Question #135383
A student taking a quiz finds on a reference sheet the two equations f = 1 / T and =square root of (1/T).
She has forgotten what T represents in each question.
Use dimensional analysis to determine the units required for T in each question.
Explain how you can identify the physical quantity each T represents from the units.
1
Expert's answer
2020-10-01T10:11:29-0400

solution

given formula


f=1Tf=\frac{1}{T}


f is the frequency so unit of frequency is s1s^{-1}

by using dimension analysis

T=1fT=\frac{1}{f}


so

[T]=1s1[ \quad T\quad]=\frac{1}{s^{-1}}


=s.

so unit of T is second and T is time.


v=Tμv=\sqrt \frac{T}{\mu}


and v is velocity and mu is linear density

T=v2μT=v^2\mu

[T]=[v2μ][\quad T\quad]=[\quad v^2\mu \quad]


[T]=m2/s2kg/m[\quad T\quad]=m^2/s^2\cdot kg/m\\


[T]=kgms2=N[\quad T\quad]=\frac{kg\cdot m}{s^2}=N

there T represents force.



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