# Work+conservation of energy

1. Dec 18, 2004

### UrbanXrisis

Sliding a block on a floor that has friction. Going from points A to B to C to D then back to A. points ABCD make a rectangle. Moving the block at a constant speed. What is the work done by the closed loop?

Since speed is a constant, then there isn't a change in KE, so then work done has to be zero right?

What if I did this on a frictionless table? Would the work done be zero as well?

2. Dec 18, 2004

### Staff: Mentor

The work done by what force? To move that block a force must be applied to overcome friction. That force does work which ends up increasing the internal energy of the block + floor. (They heat up.)

The work-energy theorem says that the work done by the net force on an object will equal the change in KE. But the net force is zero, thus no change in KE.

If you applied the same force, the block would accelerate and the work done would equal the change in KE of the block. To move the block at a constant speed requires no force (ignoring those corners!).

3. Dec 18, 2004

### arildno

"Since speed is a constant, then there isn't a change in KE, so then work done has to be zero right?"

The work of the NET force is zero, but this doesn't mean that the work from the individual forces (friction and pushing force) are each zero.
The individual forces' work is most certainly not zero, only their SUM.

Last edited: Dec 18, 2004
4. Dec 18, 2004

### disruptors

"Since speed is a constant, then there isn't a change in KE, so then work done has to be zero right?"

Work isn't zero for individual forces just like urban said. On a frictional surface conservative energy isn't conserved thus W(neoconservative)=change(mgh)+0 KE...The force is neoconservative in this case I think thus W(nc of friction)=mgh if you have those variables of h and m.

Last edited: Dec 18, 2004
5. Dec 18, 2004

### UrbanXrisis

Does this mean there is no change in KE?

6. Dec 18, 2004

### Staff: Mentor

If the net force is zero, no work is done and the KE does not change.

7. Dec 18, 2004

### UrbanXrisis

so there is no change in KE for frictionless or friction surfaces?

How do you know if energy is conserved or not?

8. Dec 18, 2004

### Staff: Mentor

If the object moves at constant speed how can the KE change?

I'm not sure what you mean:
(1) For the frictionless surface, no energy is added (no work is done by an outside force) so energy is certainly conserved.
(2) For the friction surface, work must be done by an applied force. That work goes to heat. But no net work is done on the object, so its mechanical energy is conserved.

9. Dec 18, 2004

### gschjetne

Hey, couldn't you just use this formula:
$$W = ( \mu mg \cdot \vec{F}_\textrm{normal} ) ( AB + BC + CD + DA )$$
This depends of course on what information you've got.
Edit: made a correction to the formula

Last edited: Dec 18, 2004
10. Dec 18, 2004

### delton

The formula $$W = ( \mu mg \cdot \vec{F}_\textrm{normal} ) ( AB + BC + CD + DA )$$does indeed work. But remember that work equals
force times displacement, not distance. The displacement (net distance traveled) in this case is zero, so the work is zero. If you want to show this, make CD and DA negative distances.

11. Dec 19, 2004

### gschjetne

OK, I see. Thanks for clearing that up.

12. Dec 19, 2004

### Staff: Mentor

What's this formula supposed to be? What do you mean by $\mu mg \cdot \vec{F}_\textrm{normal}$ ?