First slide

Second law

Question

A U - shaped smooth wire has a semicircular bending between A and B as shown in the figure. A bead of mass m moving with uniform speed v through the wire enters the semicircular bend at A and leaves at B. the average force, exerted by the bead on the part AB of the wire is

Moderate

A

0
B

$\large \frac {4mv^2}{\pi d}$
C

$\large \frac {2mv^2}{\pi d}$
D

$\large \frac {mv^2}{\pi d}$

Solution

$\large F = \frac{{2mv}}{t} = \frac{{2mv}}{{\left( {\frac{{\pi d}}{{2v}}} \right)}} = = \frac{{4m{v^2}}}{{\pi d}}$

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