Calculate Force Applied by Pendulum

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SUMMARY

The calculation of force applied by a pendulum involves understanding its potential and kinetic energy. When a pendulum of length l is raised to an angle θ and released, its potential energy is calculated using the formula mgh = mgl(1 - cos(θ)). At the lowest point, this potential energy converts to kinetic energy, represented as (1/2)mv² = mgl(1 - cos(θ), leading to the velocity formula v² = 2gl(1 - cos(θ)). The resulting momentum at the bottom is mv = m√(2gl(1 - cos(θ)), but the impact force depends on the specifics of the collision.

PREREQUISITES
  • Understanding of basic physics concepts such as potential and kinetic energy
  • Familiarity with pendulum mechanics and motion
  • Knowledge of momentum and its calculation
  • Basic trigonometry for angle calculations
NEXT STEPS
  • Research the principles of energy conservation in pendulum motion
  • Learn about impulse and its effect on collision forces
  • Study the effects of different collision types (elastic vs. inelastic) on force calculation
  • Explore advanced pendulum dynamics and their applications in real-world scenarios
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Physics students, engineers, and anyone interested in mechanics, particularly those studying pendulum dynamics and collision forces.

crashnelson
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how do I calculate the force applied to a target using a pendulum of known weight, angle and lever arm?
 
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A little more information would be nice. I take it you are lifting the pendulum to some specified angle and releasing it so that it strikes an object at the bottom?

You can calculate its speed and momentum at the bottom by finding the potential energy when released: If the pendulum has length l and is raised an angle θ, then it potential energy is mgh= mgl(1- cos(θ)). At the bottom its potential energy is 0 so its kinetic energy is (1/2)mv2= mgl(1- cos(θ)) or v2= 2gl(1- cos(&theta)). Its momentum would be mv= m√(2gl(1- cos(&theta)).

How much force that would hit something with depends upon exactly how the collision occurs. Does the pendulum come to a stop? How long does the collision continue?
 

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