The partial derivative with respect to one variable is taken with the other variable held constant. So [itex]\partial U/\partial x = 2kx\hat x[/itex] and [itex]\partial U/\partial y = 2ky\hat y[/itex].pittuniv said:Homework Statement
U = k(x^2 + y^2) What is the force exerted on the particle?
Homework Equations
F = -(∂U/∂x ihat +∂U/∂y jhat +∂U/∂z khat) <--couldnt get the del symbol right
determining force from potential energy
The Attempt at a Solution
F = -∂/∂x[k(x^2+y^2)]ihat - ∂/∂y[k(x^2 +y^2)]jhat
=-[2kx + Y^2]ihat - [kx^2 + 2ky]jhat
Im new to calculus, and I am pretty sure that I am not doing the derivative of this right...any help would be greatly appreciated.
Potential energy is the stored energy an object has due to its position or configuration. It is often described as the energy that an object has the potential to release or use.
The potential energy of a particle moving in one-dimension is related to its position along the dimension. As the particle moves, its potential energy may change depending on its position relative to other objects with which it may interact.
The potential energy function of a particle is a mathematical representation of the potential energy of a particle in terms of its position along a given dimension. It may take the form of a graph or equation.
The potential energy of a particle can be affected by its mass, the strength of the forces acting on it, and its position relative to other objects or forces. Additionally, potential energy can be influenced by external factors such as temperature and pressure.
Potential energy is the stored energy of an object, while kinetic energy is the energy of motion. Potential energy can be converted into kinetic energy and vice versa, but they are distinct forms of energy.