Hello!
Anyone can help me this problem? A single conservative force F(x) acts on 2.0 kg particle that moves along an x-axis. The potential energy U(x) is given by U(x)= -5xe^(-x/5) where x is in meter at x=1.0 m, the particle has kinetic energy of 4 J.
a) What is the total mechanical energy of the particle?
b) Determine the position where the particle is in equilibrium when F(x)= 0.

Question

Hello!
Anyone can help me this problem? A single conservative force F(x) acts on 2.0 kg particle that moves along an x-axis. The potential energy U(x) is given by U(x)= -5xe^(-x/5) where x is in meter at x=1.0 m, the particle has kinetic energy of 4 J.
a) What is the total mechanical energy of the particle?
b) Determine the position where the particle is in equilibrium when F(x)= 0.

anonymous · Answer

(a)Because F is a conservative force, like gravity, or spring force, by energy of conservation, E(total)= Ek(4)+U(4)
(b)By F(x)=-dU(x)/dx=0, find x