PHYS 301
HOMEWORK #1
Due : Beginning of class on Monday, 31 Jan. 2011
Please review the requested format for submitting homework described in the course syllabus. Your answers
must show clearly and completely how you arrive at your answers in order to receive full credit. Homeworks
must be submitted at the beginning of class on the due date; no homeworks will be accepted for grading once I
change the permissions on the course website making the solutions viewable to the public.
1. What is the numerical value of the expression:
dij d jk dkm dim
where the d are Kronecker deltas.
2. Consider a vector A(t). A(t) has a constant magnitude and is a function of time. (Think about an example
of a time varying vector that has constant length). Show that A(t) is perpendicular to dA(t)/dt.
3. Evaluate eijk d jk where e is the Levi-Civita permutation tensor and d is the Kronecker delta.
4. The position vector of a particle as a function of time is given by :
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r = cos t x + sin t y + t z
Show that both the speed and magnitude of acceleration are constant.
5. A force described by :
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F = x 3 x + x2 y + 2 y
pushes an object along the + x axis from x = 2 to x = 4. Evaluate how much work the force does
on the object.
6. Use Mathematica for this question. Print out your Mathematica results and attach them to
this HW assignment. Define 3 different three dimensional vectors (a, b, c) such that no vector is
a multiple of any other. Use Mathematica to show that
a ÿ bäc = | c·(aäb) |=| b·(cäa) |