How Does Non-Conservative Force Affect Mechanical Energy Along Different Paths?

[keltix]

Homework Statement

Figure 8-17 shows one direct path and four indirect paths from point i to point f. Along the direct path and three of the indirect paths, only a conservative force Fc acts on a certain object. Along the fourth indirect path, both Fc and a conservative force Fnc act on the object. The change in ME (in Joules) in going from i to f is indicated along each straight line segment of the indirect paths.
(a) what is change in ME in moving from i to f along the direct path
(b) what is change in ME due to Fnc along the one path where it acts.

This is a conceptual question but I don't get it.

Homework Equations

change in ME=change in K + change in U=0

The Attempt at a Solution

Change in ME should equal zero for conservative forces. But the diagram has a bunch of numbers that neither add up to zero or are 0.

http://i2.photobucket.com/albums/y25/keltix/fig8-17question1.jpg"

 

[keltix]

anyone please

 

[dotman]

Hello,

Seems to me they're asking what happens to the energy along the four paths (3 indirect and 1 direct) where only a conservative force acts, and what happens along the other indirect path where two forces act.

I see three indirect paths that have something in common, and one that doesn't. Can you spot it?

 

[keltix]

Yea, the brown/red path is 10J so that is one on which the non-conservative force acts upon right?

But on the other ones where only the conservative force acts, why does it change MECHANICAL ENERGY if it is a conservative force?

 

[dotman]

Hello,

Yeah, that's what I saw too. The one path has a different energy change-- the non conservative force.

Now, a conservative force doesn't mean that the energy won't change going from one point to another-- what it means is that if you go from point A to point B, and then back, you're going to have the same energy at point A as you started with regardless of the path you take. Check this out, it's got a decent description:

http://hyperphysics.phy-astr.gsu.edu/hbase/pegrav.html#cfor"

 

[keltix]

Weird.

So let's say gravity (a conservative force) was the force that acted upon those 3 paths.
How would it add 12J of ME.

Also, I thought that the whole point of conservation of energy meant that ME1=ME2 so change would be zero.

 

[dotman]

Yeah, you're right about the conservation of energy stuff. Are you sure when they say ME (mechanical energy? never heard it called that) they're not talking just about the kinetic energy? Or just about the potential energy?

Because you're right, the energy from point i to point f should simply be transferred between the two, and recovered on the reverse path.

Edit: When I say recovered, I mean the potential energy recovered from the kinetic of course. And I should have said 'a' reverse path, since pathing is irrelevant.

 

[keltix]

The numbers on the line segments are CHANGE in ME.

I'm going to ask my teacher and see what she thinks. Thanks.