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Qmechanic ♦
Qmechanic ♦
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I'm a maths student taking a course in classical mechanics and I'm having some confusion with the definition of a potential.

If we consider a simple pendulum then the forces acting on the end are $mg$ and $T$. Now I know that the potential is defined such that $F = -\nabla V$. Now I also know that the total energy of this system is $\frac{1}{2}m \dot{\vec{x}}^2 + mgz$.$$\frac{1}{2}m \dot{\vec{x}}^2 + mgz.$$ Now if we take the gradient of the potential we have $(0,0,mg)$. My question is, why doesn't the potential involve the tension in the pendulum?

Thanks

I'm a maths student taking a course in classical mechanics and I'm having some confusion with the definition of a potential.

If we consider a simple pendulum then the forces acting on the end are $mg$ and $T$. Now I know that the potential is defined such that $F = -\nabla V$. Now I also know that the total energy of this system is $\frac{1}{2}m \dot{\vec{x}}^2 + mgz$. Now if we take the gradient of the potential we have $(0,0,mg)$. My question is, why doesn't the potential involve the tension in the pendulum?

Thanks

I'm a maths student taking a course in classical mechanics and I'm having some confusion with the definition of a potential.

If we consider a simple pendulum then the forces acting on the end are $mg$ and $T$. Now I know that the potential is defined such that $F = -\nabla V$. Now I also know that the total energy of this system is $$\frac{1}{2}m \dot{\vec{x}}^2 + mgz.$$ Now if we take the gradient of the potential we have $(0,0,mg)$. My question is, why doesn't the potential involve the tension in the pendulum?

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Wooster
Wooster
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Confusion with potential in simple pendulum

I'm a maths student taking a course in classical mechanics and I'm having some confusion with the definition of a potential.

If we consider a simple pendulum then the forces acting on the end are $mg$ and $T$. Now I know that the potential is defined such that $F = -\nabla V$. Now I also know that the total energy of this system is $\frac{1}{2}m \dot{\vec{x}}^2 + mgz$. Now if we take the gradient of the potential we have $(0,0,mg)$. My question is, why doesn't the potential involve the tension in the pendulum?

Thanks