How is potential energy (U) mathematically related to force (F)?
Understand the Problem
The question is asking about the mathematical relationship between potential energy and force, likely in the context of physics. It seeks to identify the correct formula from the provided options that expresses this relationship.
Answer
F(x) = -dU/dx
The mathematical relationship between potential energy (U) and force (F) is given by F(x) = -dU/dx, where F(x) is the force as a function of position, and U is the potential energy function.
Answer for screen readers
The mathematical relationship between potential energy (U) and force (F) is given by F(x) = -dU/dx, where F(x) is the force as a function of position, and U is the potential energy function.
More Information
In a conservative force field, the force is the negative spatial derivative of the potential energy. This principle is particularly relevant in contexts such as gravity, springs, and electric fields.
Tips
A common mistake is to forget the negative sign, which indicates that the force acts in the direction that decreases the potential energy.
Sources
- 2.5: Force and Potential Energy - Physics LibreTexts - phys.libretexts.org
- Relation between potential energy and forces - Physics Stack Exchange - physics.stackexchange.com
- What is the relationship of potential energy to conservative force? - Vaia - vaia.com
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