Engineering Assignment

ENGR 112 HW#2 NAME________________________

1. Determine the fundamental dimensions of V (this symbol does not represent velocity or volume) in the following equation for a pendulum:

·g·L·cos θ V = − m where m is the pendulum mass, g is the acceleration of gravity, L is the pendulum length and θ is the angular position of the pendulum. 2. The equation

E ·F )· A = ( − 2 √ D2·B·C has terms that have the following fundamental dimensions:

D C EB = M L t2 2

= L3 M = L = L

If the equation is dimensionally homogeneous, what are the fundamental dimensions of A and F? 3. The thrust propelling a rocket is given by the equation

NF = n √kRT where ​R​ is a gas constant which for air is 53.35 ft ⋅ lbf / (lbm ⋅°R); ​k​ is a dimensionless ratio; ​T​ is the air temperature (°R); and ​N​ is a dimensionless mach number. What are the fundamental dimensions of ​n​ and what does ​n​ physically represent? 4. In the following dimensionally homogeneous equation ​P​ is a pressure; ​F​ is a force; ​y​, r​, and ​h​ are lengths; ​C​ is a reciprocal length and ​α​ and ​β​ are angles. What are the fundamental dimensions of ​S​?

· ·(sin 2α sin β )P = F ·y C·S4

r h +

5. Perform the following conversions, using the ​cancellation of units method​. ​(Show your work for credit) ).​ Use additional paper as needed.

1) 853 in to yd.

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ENGR 112 HW#2 NAME________________________

2) 25.6 sec to hr

3) 0.256 yd​3​ to in​3

4) 56.2 cm to mm

5) 25,800 cm to km

6) 25.6 Liters to m​3

7) 3.58 ft​3​ to Liters

8) 0.556 yd to cm

9) 30 gal to Liters

5. Continued. Perform the following conversions, using the ​cancellation of units method​. ​(Show your work for credit) ).​ Use additional paper as needed.

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ENGR 112 HW#2 NAME________________________

10) 25.2 mi to km

11) 526 cm​2​ to ft​2

12) 5.21 km​2​ to mi​2

13) 536 in​2​ to m​2

14) 6.25 g/cm​2​ to mg/mm​2

15) 7.36 ft/sec to mi/hr

16) 62.3 acre to km​2

17) 59.3 gal/min to L/sec

18) 95.6 kg/m​3​ to mg/cm​3

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