Is the work done by friction on a moving car's wheel positive or negative?

[songoku]

Homework Statement

The work done of friction is always:
a. positive
b. negative
c. zero
d. any of these

Relevant Equations

W = F.d

The answer key is (b) but in my opinion it should be (d) because I think about work done by friction on wheel of car when the car moves. Let say the car moves to the right, then the wheel will rotate clockwise and the direction of friction acting on the wheel by the road will be to the right and since the displacement is also to the right the work done by friction on the wheel is positive.

Am I missing something? Thanks

 

[Steve4Physics]

I agree. And note that the work done by friction can also be zero, e.g. a car parked using its brakes on a hill.

I think the question is badly written and should include a phrase such as “when sliding occurs”. [Edited.]

 

[jbriggs444]

Even when sliding occurs, the work done by friction on a particular object can be positive.

Take, for example, a child who is running rearward in the aisle on an airliner and who then slides to a stop next to the rear lavatory. The force of kinetic friction from the floor on the child's feet acts forward -- in the direction of the child's net motion, increasing the child's net velocity and ground-relative kinetic energy and doing positive work [in the ground frame]. Both energy and work are frame-relative numbers.

What is true is that if one counts both third law partner forces in the interaction, sliding friction always drains mechanical energy from the system. The net is negative work done. Or zero in the case of static friction. The net work done is an invariant quantity. It does not change depending on the chosen frame of reference.

 

[Delta2]

I think friction's positive work is called pseudo-work, I wonder why.

 

[Orodruin]

It all boils down to the force being frame independent but the displacement being frame dependent. There is no such thing as ”work done by friction” without reference to a frame. You can always choose that frame such that the work done by friction is positive, negative, or zero.

 

[robphy]

Possibly interesting:
https://brucesherwood.net/?p=134

You’ll find links to two articles
https://brucesherwood.net/wp-content/uploads/2017/06/Pseudowork1983.pdf
https://brucesherwood.net/wp-content/uploads/2017/06/Friction1984.pdf
which have been on my to-read list.

 

[jbriggs444]

You’ll find links to two articles
https://brucesherwood.net/wp-content/uploads/2017/06/Pseudowork1983.pdf

Ahhh, so "pseudowork" means "center of mass work". That seems easy enough.

 

[songoku]

Thank you very much for the explanation Steve4Physics, jbriggs444, Delta2, Orodriun, robphy