Physics Dimensional Analysis

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1. The speed of sound in air is 767 miles per hour.  Use unit conversions to determine:  a) the speed of sound in meters per second  b) the speed of sound in kilometers per hour, and  c) the speed of sound in feet per minute.
2. A basketball court is 4,700 square feet.  Use unit conversions  to determine:  a) The area in square meters  b) the area in square inches, and c) the area in acres.
3. A bucket has a base with a diameter of 8.0 in.  How high do you need to fill the bucket to get 2.0 L of water?
4. Density (p) has units of kg/m3.  Area (A) has units of m2.  Mass (m) has units of kg.  Height (h) has units of m.  Use dimensional analysis to determine which of these equations can be used to calculate the height of a object and which cannot.
a) h equals m over A rho
b) h equals m over rho A
c) h space equals space fraction numerator m over denominator rho A end fraction
d) h equals rho over m A
5. The equations that relates length (x), time (t), and acceleration (a) is x = 1/2 a t2.  If length is in units of meters (m) and time is in units of seconds (s), use dimensional analysis to determine the units of acceleration.
6.  Describe an example of an application of a unit that you might see in your future career.  List the object being measured, the property, and the units (including any prefixes).  Do not use any examples from the textbook or lecture.

 

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