Apendulum consists of a small object hanging from the ceiling at the end of a string of negligible mass. the string has a length of 0.79 m. with the string hanging vertically, the object is given an initial velocity of 1.1 m/s parallel to the ground and swings upward in 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.

θ = 21.7 °.

Explanation:

Let the length of the pendulum be L. . Initial kinetic energy of pendulum

is 1/2 mv² . Initial  potential energy is zero .

The distance by which  the bob of pendulum is raised

= L - Lcosθ

= L (1 - cos θ )

Increase in potential energy = mgL(1- cosθ )

According to conservation of mechanical energy

1/2 mv² = mgL ( 1 - cos θ)

v² = 2gL(1-cosθ)

Putting the values of different variables given

( 1.1 )² = 2 x 9.8 x .79 (1-cosθ)

(1-cosθ) = .071

cosθ = .929

θ = 21.7 °.

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