A pendulum consists of a small object hanging from the ceiling at the end of a string of negligible mass. The string has a length of 0.75 m. With the string hanging vertically, the object is given an initial velocity of 2.0 m/s parallel to the ground and swings upward on a circular arc. Eventually, the object comes to a momentary halt at a point where the string makes an angle θ with its initial vertical orientation and then swings back downward. Find the angle θ.

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Asked Oct 15, 2019
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A pendulum consists of a small object hanging from the ceiling at the end of a string of negligible mass. The string has a length of 0.75 m. With the string hanging vertically, the object is given an initial velocity of 2.0 m/s parallel to the ground and swings upward on a circular arc. Eventually, the object comes to a momentary halt at a point where the string makes an angle θ with its initial vertical orientation and then swings back downward. Find the angle θ.

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Expert Answer

Step 1

Given,

Length of the string / 0.75 m
Velocity of the object v = 2.0 m/s
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Length of the string / 0.75 m Velocity of the object v = 2.0 m/s

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Step 2

Diagram,

В
D
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В D

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Step 3

Let the final speed of the object is zero at point A and take D point ...

Initial K.E. Initial Potential Energy Final K.E. +Final Potential Energy
1
mv2=mgh
h=
2g
(2)
h=
2*9.8
h 0.204 m
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Initial K.E. Initial Potential Energy Final K.E. +Final Potential Energy 1 mv2=mgh h= 2g (2) h= 2*9.8 h 0.204 m

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