Calculate Force from Energy of a Particle

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SUMMARY

The discussion focuses on calculating force from the energy of a particle, specifically using the formula for potential energy in a spring, expressed as E = k*(|x1-x2| - L)^2, where k is the stiffness and L is the rest length. The internal force can be derived from the potential energy using the equation internal force = -d(potential energy)/dx, leading to the expression internal elastic force = -kx. Additionally, the discussion touches on more complex scenarios, such as bending rods, where energy is expressed as E = k(theta - original theta), incorporating angular displacement.

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  • Understanding of potential energy and its mathematical representation
  • Familiarity with Hooke's Law and spring mechanics
  • Knowledge of calculus, specifically differentiation
  • Basic principles of mechanics, including forces in gravitational fields
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  • Study the derivation of force from potential energy in various mechanical systems
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ila1985
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If I have a energy of a particle and I need to calculate the expression for force on it how do i do it.

eg: energy of a spring = k*(|x1-x2| - L )^2

where x1 and x2 are particle at end of the springs and K is stiffness. L rest length.
 
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ila1985 said:
If I have a energy of a particle and I need to calculate the expression for force on it how do i do it.

eg: energy of a spring = k*(|x1-x2| - L )^2

where x1 and x2 are particle at end of the springs and K is stiffness. L rest length.

I think it is better to start with
internal force=-d(potential energy)/dx
potential energy=kxx/2
internal elastic force -kx
In the gravitational field
Energy mgx
Force -mg
 
Thanks bernhard. What i was wondering is if it is more complicated force like rod bending where energy is given by E = k (theta - original theta)
and new theta is given by tan(inverse) [ (x1-x2)x(x2-x3)/(x1-x2).(x2-x3))]
x -> cross prdt
. -> dot prdt

and X1 and X2 are joined with a rod. and X2 and X3 re joined with a rod. K is stiffness
 

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