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With
L
= 1.20 m, we have
d
= 0.60(1.20 m) = 0.72 m.
Notice that if
d
is greater than this value, so the highest point is lower, then the speed of
the ball is greater as it reaches that point and the ball passes the point. If
d
is less, the ball
cannot go around. Thus the value we found for
d
is a lower limit.
68. We use conservation of mechanical energy: the mechanical energy must be the same
at the top of the swing as it is initially. Newton's second law is used to find the speed, and
hence the kinetic energy, at the top. There the tension force
T
of the string and the force
of gravity are both downward, toward the center of the circle. We notice that the radius of
the circle is
r
=
L
–
d
, so the law can be written
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This note was uploaded on 05/17/2011 for the course PHY 2049 taught by Professor Any during the Spring '08 term at University of Florida.
 Spring '08
 Any
 Physics, Energy, Force, Kinetic Energy

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