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Power of a variable from dimensions
Related Topics
Wize University Physics Textbook (Master) > Foundations / Introduction / Measurement
Units
3 Activities
If the dimensions of the variables
W
=
[
L
3
]
,
X
=
[
M
T
]
,
Y
=
[
M
6
L
]
,
Z
=
[
M
2
T
]
W=[L^3]\ ,\ X\ =\left[\frac{M}{T}\right]\ ,\ Y=\left[\frac{M^6}{L}\right],\ Z\ =\left[M^2T\right]
W
=
[
L
3
]
,
X
=
[
T
M
]
,
Y
=
[
L
M
6
]
,
Z
=
[
M
2
T
]
What is the exponent n?
12
X
3
W
=
Y
3
Z
n
\frac{12X^3}{\sqrt{W}}=\frac{\sqrt{Y^3}}{Z^n}
W
12
X
3
=
Z
n
Y
3
1
2
3 50 40 depending on, We need
4
5
I don't know
Check Submission
More Units Questions:
Dimensions and units of a constant
This is the Stefan-Boltzmann equation.
σ
\sigma
σ
is the Stefan-Boltzmann constant.
P
A
=
σ
T
4
\frac{P}{A} = \sigma T^4
A
P
=
σ
T
4
a) Knowing that
P
=
[
M
L
2
T
3
]
P = [\frac{ML^2}{T^3}]
P
=
[
T
3
M
L
2
]
is power,
A
=
[
L
2
]
A = [L^2]
A
=
[
L
2
]
an area, what are the dimensions of the constant?
Finding the exponent from dimensional analysis
X
=
Y
Z
32
W
n
X = \frac{Y Z}{32 W^n}
X
=
32
W
n
Y
Z
If
X
=
[
M
θ
]
X = [M\theta]
X
=
[
M
θ
]
,
Y
=
[
M
T
2
]
Y = [MT^2]
Y
=
[
M
T
2
]
,
Z
=
[
θ
/
L
2
]
Z = [\theta / L^2]
Z
=
[
θ
/
L
2
]
, and
W
=
[
T
/
L
]
W = [T/L]
W
=
[
T
/
L
]
, what is the exponent n?
Dimensions and units of a constant
This is the Stefan-Boltzmann equation.
σ
\sigma
σ
is the Stefan-Boltzmann constant.
P
A
=
σ
T
4
\frac{P}{A} = \sigma T^4
A
P
=
σ
T
4
a) Knowing that
P
=
[
M
L
2
T
3
]
P = [\frac{ML^2}{T^3}]
P
=
[
T
3
M
L
2
]
is power,
A
=
[
L
2
]
A = [L^2]
A
=
[
L
2
]
an area, what are the dimensions of the constant?
Counting heartbeats
How many times does your heart beat in a year?
Fermi question: paperclips
How many paperclips can you fit in an average cup (1 m
3
=1000 L)?
Filling your tub
How much water (in m
3
) can you keep in your bathtub without it spilling?
Let's say you are a really fast runner. I mean, like 50km/h fast. Convert that into the following units.
Symbols
In dimensional analysis, the symbol for time is
T
, for mass is
M
, for length is
L
.
In the SI unit system, the symbol for nanogram is
ng
, for millikelvin is
mK
, and centinewton is
cN
.