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The mass of pendulum bob is 100g.Length of pendulum is 1m.The bob is drawn aside feom equilibrium position so that it makes angle of 60 with the vertical let go.The kinetic energy of the bob while crossing the equillibrium position will be???? PLEASE GIVE A DETAILED SOL.
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The mass of pendulum bob is 100g.Length of pendulum is 1m.The bob is d...
Given Data
- Mass of pendulum bob (m) = 100 g = 0.1 kg
- Length of pendulum (L) = 1 m
- Angle with the vertical (θ) = 60°
Potential Energy at Maximum Displacement
When the pendulum bob is at the maximum displacement (θ = 60°), it has maximum potential energy and zero kinetic energy. The height (h) gained by the bob can be calculated using:
- h = L - L * cos(θ)
- h = 1 - 1 * cos(60°)
- h = 1 - 1 * (1/2) = 1 - 0.5 = 0.5 m
The potential energy (PE) at this position is given by:
- PE = m * g * h
- PE = 0.1 kg * 9.81 m/s² * 0.5 m
- PE = 0.4905 J
Kinetic Energy at Equilibrium Position
As the bob swings down to the equilibrium position, all potential energy converts to kinetic energy (KE). Therefore, at the equilibrium position:
- KE = PE at maximum displacement
- KE = 0.4905 J
Conclusion
Thus, the kinetic energy of the bob while crossing the equilibrium position will be:
- KE = 0.4905 J
This result demonstrates the conservation of mechanical energy in the pendulum's motion, where potential energy is converted into kinetic energy as it swings.
- Mass of pendulum bob (m) = 100 g = 0.1 kg
- Length of pendulum (L) = 1 m
- Angle with the vertical (θ) = 60°
Potential Energy at Maximum Displacement
When the pendulum bob is at the maximum displacement (θ = 60°), it has maximum potential energy and zero kinetic energy. The height (h) gained by the bob can be calculated using:
- h = L - L * cos(θ)
- h = 1 - 1 * cos(60°)
- h = 1 - 1 * (1/2) = 1 - 0.5 = 0.5 m
The potential energy (PE) at this position is given by:
- PE = m * g * h
- PE = 0.1 kg * 9.81 m/s² * 0.5 m
- PE = 0.4905 J
Kinetic Energy at Equilibrium Position
As the bob swings down to the equilibrium position, all potential energy converts to kinetic energy (KE). Therefore, at the equilibrium position:
- KE = PE at maximum displacement
- KE = 0.4905 J
Conclusion
Thus, the kinetic energy of the bob while crossing the equilibrium position will be:
- KE = 0.4905 J
This result demonstrates the conservation of mechanical energy in the pendulum's motion, where potential energy is converted into kinetic energy as it swings.
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The mass of pendulum bob is 100g.Length of pendulum is 1m.The bob is d...
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The mass of pendulum bob is 100g.Length of pendulum is 1m.The bob is drawn aside feom equilibrium position so that it makes angle of 60 with the vertical let go.The kinetic energy of the bob while crossing the equillibrium position will be???? PLEASE GIVE A DETAILED SOL.
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The mass of pendulum bob is 100g.Length of pendulum is 1m.The bob is drawn aside feom equilibrium position so that it makes angle of 60 with the vertical let go.The kinetic energy of the bob while crossing the equillibrium position will be???? PLEASE GIVE A DETAILED SOL. for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about The mass of pendulum bob is 100g.Length of pendulum is 1m.The bob is drawn aside feom equilibrium position so that it makes angle of 60 with the vertical let go.The kinetic energy of the bob while crossing the equillibrium position will be???? PLEASE GIVE A DETAILED SOL. covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The mass of pendulum bob is 100g.Length of pendulum is 1m.The bob is drawn aside feom equilibrium position so that it makes angle of 60 with the vertical let go.The kinetic energy of the bob while crossing the equillibrium position will be???? PLEASE GIVE A DETAILED SOL..
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