Question 188.
Figure shows a bar of mass m = 0.2 kg
that can slide without friction on a pair
of rails separated by a distance l =1.2 m
and located on an incline plane that
makes an angle = 25.0° with respect to
the ground. The resistance of the resistor
is R = 1.0 and a uniform magnetic field
of magnitude of B = 0.5 T is directed
downward, perpendicular to the ground,
over the entire region through which the
bar moves. With what speed v
does the bar slide along the rails?
Answer 188.
Component of B perpendicular to the plane
= Bcos25°
=> emf induced in the coil = Bcos25°
ε = Bcos25° * 1.2 * v =
=> current in the bar,
I = ε/R = (v/R) * 1.2 Bcos25°
Force opposing the downward motion
F = I * L * Bcos25° = (v/R) * (1.2 Bcos25°)^2
As the bar starts sliding, v keeps on increasing and so does F till F balances the downward component of the weight of the bar
=> mgsin25° = (v/R) * (1.2 Bcos25°)^2
=> velocity, v
= (mgRsin25°) / (1.2 Bcos25°)^2
= (0.2 * 9.81 * 1.0 * sin25°) / (1.2 * 0.5 * cos25°)^2
= (0.8292) / (0.2957)
= 2.80 m/s.
Link to YA!
Have you ever considered using LaTeX for equation typesetting and to import the graphics to text using MathML? I wanted to suggest investigating something like LaTeXMathML ( http://www.maths.nottingham.ac.uk/personal/drw/lm.html ). Although I have never personally tried that specific tool out, it looks to be promising. I think it is possible that you may find this not only easier, but much cleaner (not to mention pretty).
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