Question

a single conservative force F(x) acts on a 1.0 kg particle that moves along the x-axis.The potential energy U(x) is given by U(x)=20+(x-2)^2 where x is in metres.At x=5.0 m the particle has a kinetic energy of 20 J
a.Make a plot of U()x) as a function of x for x>=-10 and x<=10 and on the same graph draw the line that represents the mechanical energy of the system.AND USE THIS PART TO DETERMINE
b.the least value of x
c.the greatest value of x between which the particle can move
d.the maximum kinetic energy of the particle
e.the value of x at which it occurs

Answer 1

Conservative just means that no energy is lost in the process. It's ideal. With friction, energy is lost to heat, sound, etc, never to come back to the system (they will continue to spread away). Even with a spring, there is a stiffness and you're still losing energy in similar ways. It's more accurate with particles in vacuums and force fields, but that's another story.

Total mechanical energy of the particle - I assume that is potential and kinetic energy's sum. Since we're just talking about conservative force, all the energy will stay mechanical (in the physics problems, it happens). So, the mechanical energy is constant.

Now to graphing U(x)! Just do it like any y(x) sort of thing. It's a parabola! http://www.wolframalpha.com/input/?i=U%3D20%2B%28x-2%29^2