Conservative Force: Mechanical Energy, f(x) & x Value

[hauthuong]

a single conservative force f(x) acts on a 1.0 kg particles that move along the x axis. the potential energy u(x) associated with f(x) is given by u(x)=-4xe^(-x/4) J, where x is in meters. at x=5.0 m, the particles has a kinetic energy of 2.0J. a) what is the mechanical energy of the system? determine the equation for fx as a function of xfor what x(finite)value of x does fx=0

Emech=K+U
I plugged x=5 into u(x) = -5.73
therefore Emech=2+(-5.73)=-3.73 J Is it right?
for the second one Fx= - du/dx so I come up with fx= (4-x)e^(-x/4)
and I stuck . COuld you guy give me a hint thank you

 

[da_willem]

I'm not sure about the notation, what is the difference between Fx and fx?
About your calculations, they look ok to me. And about the last question, I don't understand your problem. This one is easier than the others, so maybe you can elaborate on what the problem is.

 

[hauthuong]

I'm not sure about the notation, what is the difference between Fx and fx?
About your calculations, they look ok to me. And about the last question, I don't understand your problem. This one is easier than the others, so maybe you can elaborate on what the problem is.

I am sorry for the typo fx and Fx is the same, for the second part : x=4 so the fx=0?