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A pendulum comprising a string of length L and a sphere swings in the vertical plane. The string hits a peg located a distance d below the point of suspension (see attached)
A) show that if the sphere is released from a height below that of the peg, it will return to this height after striking the peg.
B) Show that if the pendulum is released from the horizontal position (theta = 90 degrees) and is to swing in a complete circle centered on the peg, then theminimum value of d must be 3L/5.
I've come up with the following equations that I'm trying to relate to show the height after striking the peg is the same as before.
The initial height is L  Lcos[the], the height after striking the peg is L  d  (L  d)cos[psi].
mgh(initial) = (1/2)mv^2(bottom of the arc)
mgh(final) = (1/2)mv^2(bottom of the arc).
I'm not sure where to go from here.
Any suggestions would be greatly appreciated.
Thanks.
A) show that if the sphere is released from a height below that of the peg, it will return to this height after striking the peg.
B) Show that if the pendulum is released from the horizontal position (theta = 90 degrees) and is to swing in a complete circle centered on the peg, then theminimum value of d must be 3L/5.
I've come up with the following equations that I'm trying to relate to show the height after striking the peg is the same as before.
The initial height is L  Lcos[the], the height after striking the peg is L  d  (L  d)cos[psi].
mgh(initial) = (1/2)mv^2(bottom of the arc)
mgh(final) = (1/2)mv^2(bottom of the arc).
I'm not sure where to go from here.
Any suggestions would be greatly appreciated.
Thanks.
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