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Homework assignment 1 (covers Sections 1.1, 1.2, 1.3, 1.4, 1.5, 1.6, 1.7, 1.8, 1.9, 1.10)
Due: 2:00am on Monday, April 5, 2010
Note:
You will receive no credit for late submissions.
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Grading Policy
First review Sections 1.1, 1.2, 1.3, 1.4, 1.5, 1.6, 1.7, 1.8, 1.9, and 1.10 of Young and Freedman,
including
the worked examples. You
should then be able to solve the problems given below.
Note
that you are allowed only 6 answer attempts per problem.
Dimensions of Physical Quantities
Description:
Dimensions introduced, finding dimension of physical quantities
Learning Goal:
To introduce the idea of physical dimensions and to learn how to find them.
Physical quantities are generally not purely numerical: They have a particular
dimension
or combination of dimensions
associated with them. Thus, your height is not 74, but rather 74 inches, often expressed as 6 feet 2 inches. Although feet and
inches are different
units
they have the same
dimension
--
length
.
Part A
In classical mechanics there are three base dimensions. Length is one of them. What are the other two?
Hint A.1
MKS system
The current system of units is called the International System (abbreviated SI from the French Système International). In the
past this system was called the mks system for its base units: meter, kilogram, and second. What are the dimensions of these
quantities?
ANSWER:
acceleration and mass
acceleration and time
acceleration and charge
mass and time
mass and charge
time and charge
There are three dimensions used in mechanics: length (
), mass (
), and time (
). A combination of these three dimensions
suffices to express any physical quantity, because when a new physical quantity is needed (e.g., velocity), it always obeys an
equation that permits it to be expressed in terms of the units used for these three dimensions. One then derives a unit to
measure the new physical quantity from that equation, and often its unit is given a special name. Such new dimensions are
called derived dimensions and the units they are measured in are called derived units.
For example, area
has derived dimensions
. (Note that "dimensions of variable
" is symbolized as
.) You can
find these dimensions by looking at the formula for the area of a square
, where
is the length of a side of the square.
Clearly
. Plugging this into the equation gives
.
Part B
Find the dimensions
of volume.
Hint B.1
Equation for volume
You have likely learned many formulas for the volume of various shapes in geometry. Any of these equations will give you
the dimensions for volume. You can find the dimensions most easily from the volume of a cube
, where
is the
length of the edge of the cube.
Express your answer as powers of length (