HW#1 Ch 1: Measurement
Instructions: For problems 1−3, show all work using unit conversions for full credit.
Ex: Convert 60 \(\dfrac{{mi}}{h}\) to \(\dfrac{{m}}{s}\).
\(60.0\dfrac{{mi}}{h} \cdot \left( {\dfrac{{1h}}{{3600s}}} \right) \cdot \left( {\dfrac{{1.609km}}{{1mi}}} \right) \cdot \left( {\dfrac{{1000m}}{{1km}}} \right) = 26.8\dfrac{m}{s}\)
1. Convert 25.4 \(\dfrac{{mi}}{h}\) to \(\dfrac{{m}}{s}\).
2. Convert 47.6 \(c{m^3}\) to \({m^3}\).
3. Convert 242.5 \(\dfrac{{kcal}}{month}\) to \(\dfrac{{J}}{y}\).
4. Express the following quantities in meters using scientific notation.
a) 4.58 pm b) 3.12 km c) 1.97 μm d) 7.38 nm
5. Give the dimensions of the constants C1 and C2 that appear in the following equations, if x represents distance, v represents velocity and t represents time:
a) \(v\left( t \right) = {C_1}t + {C_2}\) b) \(x\left( t \right) = {C_1}t + \dfrac{{{C_2}}}{2}{t^2}\)
c) \(v\left( t \right) = {C_1}\cos \left( {{C_2}t} \right)\) d) \(x\left( t \right) = {C_1}{e^{- C_2/t}}\)
6. Our physics classroom is roughly 18 feet x 9 feet x 36 feet, containing air that has 21% oxygen. Assume that the room is filled with 9 students and 1 professor. If the doors and windows were suddenly shut and no ventilation was provided, how long would it take before the air become hard to breathe? Assume that each person breathes 640 L of oxygen per day and that air becomes stifling at 18% oxygen. Express your answer in hours.