Work and Potential Energy Question

[Arbitrary]

Homework Statement

A 2-kg particle is acted upon by a force given by F = -100x, where F is in Newtons, while being influenced by a constant nonconservative force of 50 N. The object is released from rest at x = 5.0 m. Estimate how far the particles moves before it comes to a stop.

Homework Equations

W = \DeltaK + \DeltaU + Q
dW = F dx

The Attempt at a Solution

Since velocity = 0 when the object stops, I did:
W = 50*x
\int -100x dx = 50*x

The boundaries for integration are from 5 to x. Which leads to:

-50x^2 + 50(5)^2 = 50*x

When I solve for x, though, the answer isn't right, so obviously I did something wrong. Any hinters on what? I have a feeling it's because they're asking for how far the particle moved and not just the x location, but how would I go about finding that?

 

[Dick]

F=-100x looks like the force from a harmonic oscillator. This gives it an initial potential energy that you can calculate. I'm guessing the nonconservative force you are talking about is like friction which always acts opposite to the direction of motion. If it travels a distance d, then the energy it loses to the nonconservative force is 50N*d, right? So if you equate PE to 50N*d, you'll get something. Why don't you expect it to be exact? That's a question for you to answer.

I think you have a feeling why your attempt is wrong. The x on the left side of you equation isn't a distance, it's a coordinate (and it's also a dummy variable in an integration!), the one on the right side is. Notice the question asks for an 'estimate', not an exact solution.