# Can the work by kinetic friction on an object be zero?

We know that friction is of two types - static and kinetic. Static friction acts when there is no relative motion between the surfaces in contact. Kinetic friction takes place when surfaces rub against each other. I was wondering whether the work done by the kinetic friction can be positive, negative or zero.

• Positive work - When an object is placed on a rapidly moving belt, it moves along with the belt but with slipping (relative motion between the surfaces exist) when there is no enough friction to prevent slipping. Here the work done by the kinetic friction is positive, as the direction of frictional force and the displacement is same.

• Negative work - Work done by kinetic friction, when an object moving on a rough surface slows down, is negative as the direction of friction and displacement are opposite to each other.

I'm unable to think of any circumstances when the work done by kinetic friction is zero because of the following reasons:

• Work done on an object is zero if displacement is zero. In our case, if displacement is zero, the frictional force acting on the object is static and not kinetic in nature.

• Work done is also zero when the force and displacement are perpendicular to each other. The only example I am aware of is circular motion. As the point at which the wheel touches the ground is at rest. The nature of friction is again static.

So, can the work by kinetic friction on an object be zero?

Please note: I read the answers for the following two related questions. There is no clear explanation on the two aspects of friction (static and kinetic) in those answers. Simply they don't have enough details.

• in the positive work case that you have mentioned...if the object slips the work is negative, if the object doesn't slip its static friction right? – lineage Nov 16 at 17:10
• Work done by all dissipative forces are always negative, including kinetic friction, because they always reduces kinetic energy. When you place object on moving belt - it starts to move in opposite direction to belt speed in a belt reference frame. So belt induces kinetic friction until that object comes to rest in belt reference frame. So the same $W < 0$ situation here – Agnius Vasiliauskas Nov 16 at 17:13
• @AgniusVasiliauskas Why not post your comment as an answer? – Bob D Nov 16 at 21:22
• @Bob the best reason not to is that the statement is wrong (or more generously, true only in a highly restricted sense). And this is an important issue because there are more subtle issues surrounding the work-energy theorem that can only be resolved if you really get that work and kinetic energy are frame dependent. – dmckee Nov 16 at 22:27

Hold a piece of wood against a sanding belt. In your frame, the block is not moving, but

• kinetic friction is exerting a force: you have to hold the block still

• energy is transferred: the block gets hot, and pieces are pulled off it

Yes work done by kinetic friction may be zero for example:- consider a block slipping on ground work done by kinetic friction will be negative in ground frame but now observe the block w.r.t block itself now work done by each and every force will be zero as displacement of block w.r.t itself is zero.

• This example is very tricky if the block is accelerating. – dmckee Nov 16 at 22:30

Kinetic friction

1. is a dissipative force
2. opposes relative motion.

A "kinetic frictional force" that does no work is non-dissipative and not friction at all. Such a force has absolutely no impact on the velocity of the object.

Kinetic friction always does work for any non-zero distance.

• Kinetic energy is not invariant, and depends upon frame of reference. Kinetic friction can certainly do work. – Adrian Howard Nov 16 at 20:03

Work done by all dissipative forces are always negative, including kinetic friction, because they always reduces kinetic energy. When you place object on moving belt - it starts to move in opposite direction to belt speed in a belt reference frame. So belt induces kinetic friction until that object comes to rest in belt reference frame. So the same $$𝑊<0$$ situation here

• Work is always frame dependent. There are frame where dispositive work is positive. Standard classroom example: I drop a box straight down onto the moving belt at the grocery store. As measured in my frame the work done on the box by friction is positive. – dmckee Nov 16 at 22:18
• I know this. But in my opinion, for describing some things one frames are more "natural" than the others. In your reference frame, friction would be not a dissipative force as it should be and it's weird. Besides in your reference frame, you can't explain why friction force stops doing positive work and accelerating box after achieving $v_{max}$ speed for a box. No reasons for that, unless for this explanation you include belt reference frame too. Thus it's more natural for belt-box system. – Agnius Vasiliauskas Nov 17 at 8:34
• Friction is a disipative force in every frame, but that is not defined by doing negative work. It is defined by converting energy in coherent channels into thermal channels. And while there certainly are natural frame and unnatural frames for various problems it is important to frame your process in terms that are correct in all frames. – dmckee Nov 18 at 20:56
• Are you serious ? Many physics laws are invariant in inertial reference frames, but they are not in non-inertial ones. Some may be invariant in sub-luminal speed frames only. Others have yet more specific conditions, such as quantum mechanics laws where reference frame meaning is blurred under quantum uncertainty principle, entanglement, etc. What you want to achieve is a holy grail in physics which is surreal – Agnius Vasiliauskas Nov 19 at 7:23