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NAME: ________________________________________
LAB 1 :: DIMENSIONAL ANALYSIS
- Convert 2.54 km to inches. (2 pts)
- Convert 12.5 km/million years to mmโ
yr-1^ (3 pts)
- Convert 6.5 milesโ
decade-1^ to mโ
s-1^ (3 pts)
- While walking through the halls of Rankin Science South, you find a random piece of paper from one of Dr. Marshallโs research notebooks with several measurements listed. Based on the units, what basic types of measurements were being made? a) 3.56 x 10^3 m^2 (1 pt)
b) 3.06 gโ
cm-3^ (1 pt)
c) 4.25e6 gโ
mโ
s-2^ (2 pts)
The following questions involve using dimensional analysis. For full credit you must show your work very clearly. Also, be sure and circle your final answers. (40 pts)
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- Determine if the following equation is dimensionally homogeneous. If the equation is not dimensionally homogeneous, explain why. (2 pts)
where L = length, v= velocity, t=time, and m=mass
- A simple form of the equation for one-dimensional strain (commonly called stretch), ฮต , is given by: (2 pts)
where โ๐ is the change in length of an object and ๐ 0 is the original length of the object. What are the units of strain?
- Given the following geophysical equation (which you will see many times later in this semester),
๐๐๐^
where ๐ฅ and โ 1 are distances, and ๐ฃ 1 and ๐ฃ 2 are velocities, what type of dimension does this equation describe? In other words, what physical quantity must ๐ represent? (2 pts)
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- The surface displacement rate, Ux (i.e. a velocity), of the ground around an infinitely long and vertical strike- slip fault during the interseismic period (time between earthquakes) is given by
Where ๐ is the fault slip rate (i.e. a velocity), ๐ฅ is the distance away from the fault, and ๐ท is the locking depth of the fault. a) Given that โ๐๐๐๐ก๐๐โ is an inverse trigonometric function, what units must the result of the quantity (^) ๐ท๐ฅ have? Why? (2 pt)
b) What units must the result of ๐๐๐๐ก๐๐ (๐ฅ๐ท) return in this equation? How do you know that this is correct? Hint: there are two mathematically viable possibilities, but only one is correct! If you are lost, try doing dimensional analysis on the sohcahtoa equations. (2 pt)
c) Of ๐๐ฅ, ๐, ๐ฅ, ๐๐๐ ๐ท which variables must have identical units and which are not required to be the same? Explain your reasoning. (2 pts)
d) Slip rate is most commonly quoted in mmโyr-1^ while locking depth is most commonly quoted in km. Is this a problem in this equation? If it is a problem, what must be converted and why? (2 pt)
