# Determine the fundamental dimensions of V (this symbol does not represent velocity or volume) in the following equation for a pendulum: ? = −? ∙ ? ∙ ? ∙ cos ? 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.

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:

? = −? ∙ ? ∙ ? ∙ cos ? 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

? = (? − 2 ∙ ?) ∙ √ 2 ∙ ? ∙ ?

?

has terms that have the following fundamental dimensions:

? = M

L2t2 ? =

M

L3 ? = 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

? = ??√???

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?

? = ? ∙ ?

? ∙ ?4 ∙

?

ℎ ∙ (sin 2? + sin ?)

ENGR 112 HW#2 NAME________________________

2

- 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.

2) 25.6 sec to hr

3) 0.256 yd3 to in3

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

ENGR 112 HW#2 NAME________________________

3

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

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