Conservative force, kinetic energy

AI Thread Summary
The discussion revolves around calculating the mechanical energy, maximum kinetic energy, and the position at which it occurs for a particle influenced by a conservative force with a specified potential energy function. The mechanical energy is determined using the equation Emech = K + U, where K is kinetic energy and U is potential energy. The user expresses confidence in calculating mechanical energy but struggles with finding the derivative of the potential energy function U(x) to solve for maximum kinetic energy and its corresponding position. The derivatives of exponential functions and product rules are mentioned as necessary tools for these calculations. Overall, the focus is on applying calculus to derive the necessary values from the given potential energy equation.
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Homework Statement


A single conservative force F(x) acts on a 2.4 kg particle that moves along an x axis. The potential energy U(x) associated with F(x) is given by
U(x) = -4xe-x/4
where x is in meters. At x = 5.0 m the particle has a kinetic energy of 5.2 J. (a) What is the mechanical energy of the system? (b) What is the maximum kinetic energy of the particle and (c) the value of x at which it occurs?


Homework Equations


Emech=K+U

The Attempt at a Solution


I know how to find the mechanical energy, but I don't know how to do the derivative of U(x) so that I can do b) and c) even though its simple.
 
Physics news on Phys.org
this should be enough to find it

the derivative of e^x is e^x
the derivative of f(x)g(x) = f'(x)g(x) + f(x)g'(x)
the derivative of f(g(x)) = g'(x) f'(g(x))
 

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