Review SI Units

1. Review SI Units • Time: • Mass: • Distance: • Temperature: • Charge: EGR 101

2. Important Secondary Quantities • Force: • Energy (work): • Power: EGR 101

3. Questions: • What is a kilowatt-hour? • Where is it used? EGR 101

4. In-Class Activity Policy In-class activities intended to help learn! 2-person teams, both sign names Pass in by end of class EGR 101

5. In-Class Activity #1 A study of households and businesses in the Boston, Massachusetts area found that air conditioning units were used for an average of 4600 hours per year. Determine the total annual cost of electricity required to operate a 10,000 Btu/hr air conditioning unit in the Boston area if the electric rate is $ 0.071/kWhr. EGR 101

6. Notation • The units of variables will be referred to by putting the variables in brackets • Consider the equation: v-vo = a·t • What is the equation saying? EGR 101

7. Notation (continued) • [v] will refer to the dimension of v[t] will refer to the dimension of t • In order to determine the units of an unknown (say a), we need to be able to write equations in terms of units, e.g. EGR 101

8. Rules of Homogeneity • Definition: An equation is said to be dimensionally homogeneous if all terms separated by plus and minus and equal sign have the same dimension. • Consider the previous example: • In order to be homogeneous, EGR 101

9. Rule 1 • If the dimensional quantities are replaced by their primary units the equation should reduce to an identity. • In our example, what are the primary units? EGR 101

10. Rule 2 • Dimensions do NOT add or subtract. In order to add or subtract variables, they must have the SAME units. • In our example, [v] = [vo]. If you subtract them you have no units on the left EGR 101

11. Rule 3 • Dimensions DO multiply and divide. EGR 101

12. In-Class Activities #2, #3 • If P1 = 400 W and P2 = 12 Btu/minute, what is P1+P2 in SI units? • Which, if any, of the following are correct for acceleration units:a) m/s/s b) c) d) EGR 101

13. Exercises • A relationship between Force F in (N), distance x in (m), mass M in (kg) and speed v in (m/s) is suggested as Is this equation dimensionally homogeneous? EGR 101

14. Exercises (continued) • A relationship between Force F in (N), time t in (s), mass M in (kg) and speed v in (m/s) is suggested as: Ft2 = Mv Is this equation dimensionally homogeneous? EGR 101

15. Prefixes • As you’ve already seen, we’ll deal with both very large numbers and very small numbers. • We will use scientific notation and/or engineering prefixes to represent these numbers EGR 101

16. Refresher: common prefixes T tera 1012 G giga 109 M mega 106 k kilo 103 d deci 10-1 c centi 10-2 d milli 10-3 μ micro 10-6 n nano 10-9 p pico 10-12 EGR 101

17. Examples in Engineering Notation • 2x103 Volts = • .00045 A = • 1.3x10-6 C = • 10x107 Hz = EGR 101

18. Some Quantities Must Be Dimensionless • In Calculus you will see eax • ax must be dimensionless (no units) 1/1 • Example, if x is in m, a is in 1/m • If x is in s, a is in 1/s • Some dimensionless quantities need units to make sense • Example if v = vo e-atv and vo have units volts EGR 101

19. Class Activity In an electrical circuit the current i(t) in A (Amperes) changes with time t in s according to the function i(t) = e-2t. a) How could this function be dimensionally consistent knowing that the exponential function is always dimensionless (RHS), and that i(t) is in A on the LHS? b) What are the units of the constant 2 in the exponential function? EGR 101

20. More on Units • Remember x = cos(θ)? • What are the units of θ? EGR 101

21. Angular frequency • What are the units of ω in y(t) = cos(ωt) if t has units of s? • ω is called the angular frequency • ω = 2πf EGR 101