What are the fundamental dimensions of s what is the

Question

ASSIGNMENT

SPRING TERM

For all problems, show your work to receive full credit.

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

V = -m·g·L·cosθ

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

A ≈ (E - 2F) √(2BC/D)

has terms that have the following fundamental dimensions:

B~M · L^-2 · t^-2               C~L                 D~M · L^-3                    E~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

F = η 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 η and what does η physically represent?

4. Convert the following to the same "speed unit" of your choice.  Which is the fastest?

(a) 50 centimeters per second

(b) 2.5 kilometers per hour

(c) 1 mile per hour

(d) 125 feet per minute

5.  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?

P = {(P·y) / (c·s⁴)} · (r/h) · (sin 2α + sinβ)

6.  The Units Society Empire (USE) has defined the following set of "new" units: 1 foot = 10 toes. Convert 45 toes to units of meters.

7.  What are the dimensions of the constant coefficient (k) in the following equations?

(a) Energy = k * (mass) * (temperature)

(b) Force = K * (pressure)

(c) Pressure = k * (temperature) / (volume)

8.  Which of the following are true?

a. 30 ^oC > 32 ^oF                                 b. 273 K > 460 ^oR

c. -30 ^oF > 0 ^oC                                  d. 600 K > 400 ^oC

9.  Which of the following are false?

a. 454 g = 1 lb_f                                  b. 1 slug = 32.2 lb_m

c. 1 lb_m = 1lb_f                                    d. 1000 g = 1 kg

10. The largest hailstone in the United States was 44.5 centimeters in circumference in Coffeyville, Kansas.

(a) What is the diameter of the hailstone in units of inches?

(b) What is the volume of the hailstone in units of liters?