How Does Pendulum Motion Affect Work and Kinetic Energy Calculations?

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SUMMARY

This discussion focuses on deriving the work and kinetic energy for a pendulum using the integral of force over displacement, specifically ∫force⋅ds. The participants clarify that the correct expression for work done by gravity is W = mgR(cos(θ) - cos(θ₀)), where θ₀ is the initial angle. The confusion arises when interpreting the signs of the kinetic energy change, Δk, particularly when the direction of force and displacement are aligned or opposed. Ultimately, the discussion emphasizes the importance of correctly applying the work-kinetic energy theorem and understanding the relationship between potential and kinetic energy in pendulum motion.

PREREQUISITES
  • Understanding of basic physics concepts such as work, kinetic energy, and potential energy.
  • Familiarity with integral calculus, particularly the application of integrals in physics.
  • Knowledge of pendulum mechanics and the forces acting on a pendulum.
  • Ability to interpret mathematical expressions involving trigonometric functions and their integrals.
NEXT STEPS
  • Study the derivation of the work-energy theorem in classical mechanics.
  • Learn how to apply integral calculus to problems involving forces and motion.
  • Explore the relationship between gravitational potential energy and kinetic energy in oscillatory systems.
  • Investigate the effects of different angles on the motion of pendulums and their energy transformations.
USEFUL FOR

Students of physics, educators teaching mechanics, and anyone interested in understanding the dynamics of pendulum motion and energy transformations.

  • #31
no nevermind, i think it works if you consider the dot product a distribution over a negative differential.
 
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  • #32
stateofdogma said:
no nevermind, i think it works if you consider the dot product a distribution over a negative differential.
Not sure what you mean by that, but to be clear, no, ds does not mean abs(ds). If the range "a to b" is such that the variable of integration, x say, decreases from 'lower' bound a to 'upper' bound b then dx is negative. E.g. ##\int_a^b f.dx = -\int_b^a f.dx##.
 
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