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Sorry that I skip some steps and forget to give explanation.lanedance said:can you explain what you are attempting to do? I would approach as follows
lanedance said:say phi exists then you know
[tex] F_x = \frac{\partial\phi}{\partial x}[/tex]
[tex] F_y = \frac{\partial\phi}{\partial y}[/tex]
so integrating the first gives
[tex] \phi = \int F_x dx= \int 2x cos^2y dx =?[/tex]
lanedance said:not quite as you are only integrating w.r.t. to x, so c could be a function of y
[tex] \phi = \int F_x dx= \int 2x cos^2y dx = x^2cos^2y + c(y) [/tex]
now also do it from the other direction
[tex] \phi = \int F_y dy= ?[/tex]
lanedance said:i can't quite follow your simplification, you should equate
[tex] \phi = \int F_x dx = \int F_y dy[/tex]
lanedance said:and from there you should be able to deduce withther it is possible to to solve c(x) & d(y)
athrun200 said:This is just a identity.
http://en.wikipedia.org/wiki/List_o...ouble-.2C_triple-.2C_and_half-angle_formulae"
athrun200 said:It's my first time to solve the problem like this.
So I stuck in here
I would like to ask, what's wrong with my method above?
I have solved a lot of problems by using that method.(I learn it from mathematical methods in the physical sciences Chapter 6 sec8)
Potential energy is a form of energy that an object possesses due to its position or configuration. It is stored energy that has the potential to do work.
Potential energy is the energy an object has due to its position or configuration, while kinetic energy is the energy an object has due to its motion. They are two forms of energy that can be converted into each other.
There are several types of potential energy, including gravitational potential energy, elastic potential energy, chemical potential energy, and electric potential energy. Each type is associated with a specific force or field.
The principle of conservation of energy states that energy cannot be created or destroyed, only transferred or converted from one form to another. In a closed system, the total amount of energy remains constant.
Conservative forces are forces that do not dissipate energy and can be expressed as the negative gradient of a potential energy function. This means that the work done by a conservative force is independent of the path taken, only dependent on the initial and final positions. In other words, potential energy is a measure of the work a conservative force can do on an object.