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7.85. Set Up:
At any point, the potential energy is given by
where
l
is the string length and
is the
angle the string makes with the vertical. At the top of the swing, the kinetic energy is zero while the potential energy
is a maximum since
whereas, at the bottom of travel, the kinetic energy becomes a maximum equal
to the
of the top of the swing. In terms of conservation of energy,
or
where “f “ refers to the vertical position of the pendulum and “i “ refers to top of travel.
Solve:
Solving for the velocity,
The tension in the string at this instant is found using a force balance of the weight and radial acceleration,
Reflect:
As the string passes through the vertical the ball has an upward acceleration, due to its circular motion.
Therefore, there is a net upward force and the tension is greater than the weight of the ball.
7.86. Set Up:
Since
Let
at the lowest point in a swing. Then
and
as shown in the sketch.
Solve: (a)
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 Spring '07
 Shoberg
 Energy, Kinetic Energy, Potential Energy, Work

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