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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.
1
ENGR 112 HW#2 NAME________________________
2) 25.6 sec to hr
3) 0.256 yd3 to in
3
4) 56.2 cm to mm
5) 25,800 cm to km
6) 25.6 Liters to m3
7) 3.58 ft3 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.
2
ENGR 112 HW#2 NAME________________________
10) 25.2 mi to km
11) 526 cm2 to ft2
12) 5.21 km2 to mi2
13) 536 in2 to m2
14) 6.25 g/cm2 to mg/mm2
15) 7.36 ft/sec to mi/hr
16) 62.3 acre to km2
17) 59.3 gal/min to L/sec
18) 95.6 kg/m3 to mg/cm3
3
