# Nonconservative Forces (conceptual)

I'm having problems with solving these nonconservative forces problems. The teach keeps pointing to Wnc=(KE+PE)f - (KE+PE)i

As we use this when there is friction present, I'm totally confused on where the frictional or opposing force is involved when solving. I've basically been ignoring the frictional force when solving for instance for vf, or vi, which I'm sure isn't the right way. I don't seem to be able to find an adequate explanation in the AP book or elsewhere.

## Answers and Replies

Ambitwistor
Can you give the details of a concrete nonconservative force problem you'd like to learn how to solve, and where you get stuck in understanding what's going on? Otherwise, it's hard to guess exactly what you don't understand.

Example: "A 2.1x10^3kg car starts from rest at the top of a 5.0m long driveway that is sloped at 20 degrees with the horizontal. If an average friction force of 4.0x10^3 N impedes the motion, find the speed of the car at the bottom of the driveway."

I know there's no final kinetic force, and no final potential force, so that leaves me Wnc = KEf - PEi

1/2mv^2 - mgh

h=Fsin20 (I think)

1/2mv^2 - mgh

Yeah... not sure what to do at this point, I was thinking F was also the Ff, but I don't think that's right. I think I'm having trouble with, what happened to Wnc.

mani
The term "opposing force" is confusing.
Consider a horizontal table and a block projected on it with an initial horizontal velocity. No horizontal force other than the force of friction. What is the " opposing force" here?

You may be meaning any force. If that force is a non-conservative force the work done by that will go into Wnc. The work done by the friction force - almost always negative- will of couse go into Wnc

Ambitwistor
Originally posted by Blade
I know there's no final kinetic force, and no final potential force,

(I think you mean energy, not force, and that there is no initial kinetic energy.)

so that leaves me Wnc = KEf - PEi

1/2mv^2 - mgh

Right.

Now, you have to use the additional fact that the work done by a force is force times displacement. So you also have that the nonconservative work, which is the work done by the frictional force, is

Wnc = (4.0 x 103 N) (5 m)

Set that equal to the above expression, and you can solve for v.

h=Fsin20 (I think)

I don't know what F is.

h = (5 m) sin(20)

mani
"I'm having trouble with, what happened to Wnc."

Wnc = KEf - PEi = 1/2 mv^2 - mgh
(h = L sin20, where L the length of the driveway = 5 meters)

Wnc is also = (Friction force x Distance moved in the direction of the force) = (4x 10^3 Newtons)x(-5 meter),as the direction of distance moved, 5 meter, is opposite to that of the force.

1/2 mv^2 - mg(5 Sin20) = (4x 10^3 Newtons)x(-5 meter)
u know m and g. Find v.