Unformatted text preview: atter and Matter
FB = q V Âµ B (a) It's just (b) The centripetal force is found from Newton's second law,
d
d
F = â€¦ Ã…Ã…Ã…Ã…pÃ…Ã… â€¦ = Â» Ã…Ã…Ã…Ã…Ã… Hg m vL Â»,
Ã…
dt
dt
along with the very important relation
d
v2
Â» Ã…Ã…Ã…Ã…vÃ… Â» = Ã…Ã…Ã…Ã…Ã…Ã…
Ã…
dt
r
The fact that the speed, and therefore g, is constant in time give
d
v2
F = g m Â» Ã…Ã…Ã…Ã…vÃ… Â» = g m Ã…Ã…Ã…Ã…Ã…Ã…
Ã…
dt
r (c)
First, you must recall that frequency is cycles per second. There are a couple of equations for
frequency, but
the important one here is
f = speed Ãª distance
which you might be able to guess just from units. The speed here is the speed that the particle
is moving
around the circle, the tangential speed. The distance is the circumference, how far the particle has to go to complete one
cycle. So in terms of the variables above, we have
f = Ã…Ã…Ã…Ã…Ã…vÃ…Ã…Ã…Ã…rÃ…
2p
d
Now to use (b) to get a r. Solve Â» FB Â» = â€¦ Ã…Ã…Ã…Ã…pÃ…Ã… â€¦ for r.
Ã…
dt
Â» FB Â» = q v B sin 90 Â° = q v B
since v and B are perpendicular, q is 90Â°. So we have
v2
q v B = g m Ã…Ã…Ã…Ã…Ã...
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This document was uploaded on 02/26/2014 for the course PHYS 2D at UCSD.
 Fall '08
 Hirsch
 Physics

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