Reference no: EM131028143
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 lbf b. 1 slug = 32.2 lbm
c. 1 lbm = 1lbf 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?
|
Description for your ebp project
: Write a paper of 600 words (not including the title page and reference page) on your proposed problem description for your EBP project
|
|
Design microcontroller-based string matching detector
: how you would design this microcontroller-based string matching detector. Which peripherals would you be using? What considerations would you take into account?
|
|
Acceptable on the grounds of efficiency
: Some argue that insider trading brings information to the market more quickly and thus is morally acceptable on the grounds of efficiency. Do you agree with that argument? Why or why not?
|
|
What specifications can you make for the amplifier
: Suppose that the input voltage to an amplifier has a peak amplitude of 100mVand contains components with frequencies ranging from 1 to 10 kHz. We want the output voltage waveform to be nearly identical to that of the input except with larger ampli..
|
|
What is the diameter of the hailstone in units of inches
: What are the fundamental dimensions of s? What is the diameter of the hailstone in units of inches? What is the volume of the hailstone in units of liters?
|
|
Explain the public relations plan for the organization
: Explain the Public Relations plan for the organization. Create two sales promotions for the restaurant. Identify the challenge and solution for each promotion. Include budgetary considerations. One of your neighbors has just inherited a restaurant in..
|
|
Determine the extreme values of the output voltage
: A differential amplifier has a bias current of 100 n A, a maximum offset current of 20 n A, a maximum offset voltage of 2 mV, an input resistance of 1 MΩ, and a differential gain of 1000. The input terminals are tied to ground through (exactly equ..
|
|
Two-state put option value
: We will derive a two-state put option value in this problem. Data S0 = 110; X = 120; 1 + r = 1.1. The two possibilities for ST are 140 and 100.
|
|
How many different committees are possible
: Use the fundamental counting principle to solve:How many different four-letter radio stations call letters can be formed if the first letter must be W or K?
|