Finding the potential energy of a time dependent force

F=∇U (with plus)In summary, the conversation discusses the calculation of force using the formula F=-∇U and questions the use of a negative sign instead of a positive sign. The origin of the question is to find the Lagrangian of a pendulum with a force acting on its top end. The potential energy of the object is expected to be positive if Fdx is positive.
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Homework Statement
Force on an object is F=(m*g/3) *cos(ω*t) in x direction. Find potential energy
Relevant Equations
U=- ∫(F dx) = - ∫(F*v*dt)
U=-∫F*v*dt= -∫(m*g/3)*cos(ω*t) dt = -(m*g/3 )* (v/ω )* sin(ω*t)

except that according to the official solution, I should be getting positive sign instead of negative. Am I doing something wrong?
 
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  • #2
May I ask the origin of this question?
 
  • #3
hutchphd said:
May I ask the origin of this question?

Yes, I have to find a Lagrangian of the pendulum that has a force acting on its top end (which is free to move).
 
  • #4
The change in potential energy of the object should be positive if Fdx is positive.
 
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  • #5
hutchphd said:
The change in potential energy of the object should be positive if Fdx is positive.

OK, then why are we calculating force F as F=-∇U (with minus)
 

FAQ: Finding the potential energy of a time dependent force

What is potential energy?

Potential energy is the energy that an object possesses due to its position or configuration in a force field. It is stored energy that can be converted into other forms of energy, such as kinetic energy.

How is potential energy related to time dependent forces?

In the case of time dependent forces, the potential energy of an object can change over time as the force acting on the object changes. This means that the potential energy of an object is not constant and can vary depending on the force acting on it.

How do you calculate the potential energy of a time dependent force?

The potential energy of a time dependent force can be calculated by integrating the force function with respect to the object's position. This means that the potential energy is the area under the force-position curve.

What is the relationship between potential energy and work?

Potential energy and work are closely related. Work is defined as the transfer of energy from one form to another, and potential energy is one of the forms that energy can be transferred to. When work is done on an object, its potential energy can change.

How does potential energy affect the motion of an object?

Potential energy is a type of stored energy, so it does not directly affect the motion of an object. However, changes in potential energy can lead to changes in kinetic energy, which does affect the motion of an object. For example, when an object is released from a height, its potential energy decreases and its kinetic energy increases, causing it to accelerate towards the ground.

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