Simple dimensional analysis

  • #1
Hi, sorry for asking this but my brain still seems to be on lockdown from the summer. I have a pretty good idea of how dimensional analysis works and only seem to be having issues on one type of problem currently. something like:

t=(Cm^x)(k^y)

where:
t-oscillations of mass
m-mass
spring constant-k(force/length)
C-dimensionless constant

to find x and y.

T=(M^x)(Force/L)^y=(M^x)(ML/L(T^2))^y
T=(M^x)(M/T^2)^y
T=(M^x)(M^y/T^2y)
T=(M^(x+y))(M^y/T^2y)
T(T^2y)=M^(x+y)
T^(2y+1)=M^(x+y)

Then you get

2y+1=0
x+y=0

solving for y at top equation:
y=-1/2
then plugging in for second equation you get
x=1/2

So I have that one.

Now where I'm having hangups is on one like say:

v=(CB^x)(p^y)

B-bulk modulus
p-density
c-dimensionless constant
v-velocity
Find x and y

So I know I start with:

L/T=(M/LT^2)^x(M/L^3)^y

But honestly, I get stuck at this point. I can't figure out how to get things to cancel or how to make things simplify down easier. Do I distribute the exponent? Do I multiply the left hand by a reciprocal of one of those? Honestly, I don't get how to do one like this even though I fully get the first one which is fairly similar. Any hints to nudge me in the right direction to solve this, its been bugging me for awhile now.
 

Answers and Replies

  • #2
302
0
Simplify the exponents and compare them on both sides, just like you did in the last question (for example the exponent of L must be equal on both sides.)
 

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