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

AI Thread Summary
The discussion revolves around a conservative force acting on a 1.0 kg particle along the x-axis, with the potential energy given by u(x) = -4xe^(-x/4) J. At x = 5.0 m, the particle has a kinetic energy of 2.0 J, leading to a calculated mechanical energy of Emech = -3.73 J. The force as a function of x is derived as fx = (4 - x)e^(-x/4), with participants confirming the calculations and clarifying that fx and Fx refer to the same force. The value of x where fx equals zero is determined to be x = 4. The conversation emphasizes understanding the relationship between kinetic and potential energy in the context of conservative forces.
hauthuong
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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
 
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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.
 
da_willem said:
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?
 
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