Question

A simple pendulum consisting of a mss M attached in a string of length L is released from rest
at an angle "a" (alpha). A pin is located at a distance l below the pivot point. When the pendulum swings down, the string hits the pin as shown in the figure. The maximum angle which
string makes with the vertical after hitting the pin
is​

Answer 1

★ Corrected Question :

• ➦ A simple pendulum consisting of a mass M attached in a string of length L is released from rest at an angle "a" (alpha). A pin is located at a distance l below the pivot point. When the pendulum swings down, the string hits the pin as shown in the figure. The maximum angle which string makes with the vertical after hitting the pin is ?

★ Required Solution :

✰ Value Given to us :

• ➢ Mass of pendulum = M

• ➢ Length of string = L

• ➢ Angle formed = α

✰ Understanding the concept :

• ➲ As the only external force on the system will be the normal force by the pendulum , so mechanical energy will be conserved.

✰ According to Question :

✰ By Conservation of Energy :

• ➢ Ki + Ui = Kf + Uf

• ➢ Ki = Kf = 0

• ➢ - mgLcosα = - [ mg ( l + L - l ) cos θ

• ➢vCosθ = LCosα - l / L - l

• ➢ θ = Cos-¹ ( LCosα - l ) / L - l

★ Therefore :

• ➦ The maximum angle which string makes with the vertical after hitting the pin is θ = Cos-¹ ( LCosα - l ) / L - l

• ➦ Angle = θ = Cos-¹ ( LCosα - l ) / L - l

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Answer 2

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