Problem+Set+3+-+Dimensional+Analysis


 * Solutions to Problem Set 3**

As a class, please post your answers to PS 3. Show as much detail as needed to ensure everyone can understand how you arrived at your answer. I will post my comments as needed. (M. Grdinic)

1a. 78 cm to m: I set up my conversions like this (see below), after multiplying 78 and 1, i took the product (which is 78) and divided it by 100. The centimeters unit cancels out and the final answer becomes **.78 meters** (**__Matt C.)__** 1b.200.5mL to L. I set up my conversions as 1000 mL=1 L. I multiplied 200.5 and 1, and then I took the product 200.5 and divided it by 1000. The mL units cancel out, leaving the final answer of: **0.2 L** (this is because 1000 only has 1 significant figure). 1c. 50"u" m to mm. I know that 10^6 "u"m is equal to 1 m. So if I change that conversion to fit the mm scale (which has 3 less digits), 10^3 "u"m=1mm. I multiplied 50 "u"m by 1 and using the product I divided 50 by 10^3. The result was **0.05 mm**.
 * 78cm || 1m ||
 * || 100cm ||
 * 200.5mL || 1L ||
 * || 1000mL ||
 * -Edward Kang**

1d. 750cg to g. Using the conversion factor of 100 cg=g, I set up my conversion factor. Next, I multiplied 750 by 1, then divided by 100. The result was **7.5 grams.** -Josef Niemann
 * -Edward Kang**
 * 50"u"m || 1mm ||
 * || 10^3"u"m ||
 * -Edward Kang**
 * 750cg || 1g ||
 * || 100cg ||

1e) Using formula D=Mass/volume where mass = 14.0g and D= 10.5cm3 (10.5g / cm3= 14.0g / volume cm3) 14.0/10.5 = (1.3cm3)

1f. "How many seconds are in a one 24 hour day?" Since all units of conversion have infinitely many significant digits, rounding is not necessary. After canceling units, I got 86400 seconds. (Andrew Blank).
 * 60 seconds || 60 minutes || 24 hours ||
 * 1 minute || 1 hour || 1 day ||

1g) 10mph to meters per second I set a dimensional analysis chart with the conversion factors of hours to seconds and miles to meters.
 * = 10 miles ||= 1 hour ||= 1609.344 meters ||=  || 16093.44 meters ||=   || 268.224 meters ||
 * = 1 hour ||= 60 seconds ||= 1 mile ||=  || 60 seconds ||=   ||= 1 second ||

(Marielle Billig)

2. __72 in. to mm__ Using the conversion rate of 1 inch = 25.4 millimeters, I set up a dimmensional analysis chart: I simply multiply 72 * 25.4 and get 1800 mm because 72 only has 2 significant figures. (Arin K.)
 * 72 in. || 25.4 mm ||
 * || 1 in ||

3. Use the conversion rates 1 stone=14 pounds and 1 stone=6.35029318 km

Multiply 14*14 to get 200 pounds because 14 only has 2 significant figures.
 * 14 stone || 14 pounds ||
 * || 1 stone ||

Multiply 14*6.35029318 to get 89 kg because 14 only has 2 significant figures (Ethan M.)
 * 14 stone || 6.35029318 kg ||
 * || 1 stone ||

4. 2.75 angstroms to meters

Used the conversion rate 1 meter=10^ -10 angstroms

set up a dimensional analysis chart: Multiply 2.75*10^ -10 to get .000000000275 meters because 2.75 has 3 significant figures
 * 2.75 angstroms || 10^ -10 meters ||
 * || 1 angstrom ||

-Daniel Newman