Problem Set IV Assign Sep 27, 2006
Fall 2006 Physics 200a
Figures at the end
R. Shankar
Many problems ask for answers in terms of symbols and not numbers. You may need to
invoke things like
g
in the answer even if I did not explicitly define them.
1. (i) Using the dot product show that if
A
+
B
is perpendicular to
A

B
, then
A
=
B
.(ii) Use the dot product to relate vector components (
A
x
, A
y
) in the standard
frame to
A
0
x
, A
0
y
) measured in a frame rotated counterclockwise by an angle
θ
. Use
the fact that components of a vector are just dot products with the corresponding
basis vectors:
A
x
=
A
·
i
etc.
2. If
F
(
x
) =
Ax
3
/
2
find the work done by it in moving a body from
x
= 0 to
x
=
A
.
3. You have to choose between a 225W fridge that costs $ 1150 and a 425W model
that costs $ 850.
The first runs 11% of the time and the second runs 20% of the
time. If electricity costs 9.5 cents/kWh when will you break even? (Use hours as the
unit of time at first, go to days to report final answer.)
4. See the masses in Figure (1) which start out at rest. (i) Find the velocity of the 14
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 Fall '08
 RAMAMURTISHANKAR
 Physics, Dot Product, Force, Mass, R. Shankar, maximum spring compression

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