# Morin's explanation about the work done by friction

• almarpa

#### almarpa

Member advised to use the formatting template for all homework help requests
Hello all. In his books on classical mechanics, David Morin claims that when computing the work W = F Δx done by a contact force that don’t involve any slipping, we can equivalently say that Δx is the displacement of the thing that is applying the force. Later, when analysing a wheel rolling without slipping, he says that the frition from the ground does no work on the wheel because the ground is not moving, and it acts over zero distance.

But previously, he computes the work done by the friction from the ground to an sliding block, and in this case the friction is doing work on the block, although the ground is not moving either.

Can someoune explain this to me?

Hello all. In his books on classical mechanics, David Morin claims that when computing the work W = F Δx done by a contact force that don’t involve any slipping, we can equivalently say that Δx is the displacement of the thing that is applying the force.

Can you post his exact words becsuse that doesn't make sense.

Later, when analysing a wheel rolling without slipping, he says that the frition from the ground does no work on the wheel because the ground is not moving, and it acts over zero distance.

That's correct. There is no relative motion between the contact point on the wheel and the contact point with ground. You only get relative movement when the wheel skids over the surface.

But previously, he computes the work done by the friction from the ground to an sliding block, and in this case the friction is doing work on the block, although the ground is not moving either.

In this case there is relative movement between the object and ground. It doesn't matter if one or the other is stationary with respect to something else. For example when using sand paper on wood it doesn't matters if you rub the sand paper on the wood or the wood on the sandpaper. It's the relative motion that matters.

Ok, let me post it:

In his book "problems and solutions in introductory mechanics", page 105, when discussing the general work - energy theorem, he claims:

If an object is deformable, we need to be careful about how we define work. The work is
FΔx (we’ll deal with 1-D here, for simplicity), but if different parts of the object move different
amounts, which displacement should we pick as Δx? The correct choice for Δx is the displacement
of the point in the object where the force is applied. For contact forces (like pushing or
pulling, as opposed to long-range forces like gravity) that don’t involve any slipping, we can
equivalently say that Δx is the displacement of the thing that is applying the force. If you walk
up some stairs, then the stairs do no work on you, because they aren’t moving
.

Now, in his book "Classical mechanics with problems and solutions", page 146, when discussing the general work - energy theorem, he writes:

Consider a car that is braking (but not skidding). The friction force from
the ground on the tires is what causes the car to slow down. But this force
does no work on the car, because the ground isn’t moving
; the force acts over
zero distance. So the external work is zero.

Later, he claims:

Conversely, when a car accelerates, the friction force from the ground does
no work (because the ground isn’t moving).

And what is more, he says later:

A similar thing
happens when you stand at rest and then start walking. The friction force from
the ground does no work on you, so your total energy remains the same.

So it seems that in rolling without slipping (and when you walk up the stairs, or walk on the ground), friction from the ground does no work, because ground is not moving. Nevertheless, when a block is sliding on the ground, the ground is not moving, either. But in this case, I know that friction from the ground does work. How can Morin fit both reasonings? I do not understand it.

Thank you so much.

By the way, this is not homework help, this is just a doubt about the theory part in Morin's book. That is the reason why I did not use the template.

In the case of climbing stairs friction isn't really involved. To see what's happening you have to look at the forces that occur while the foot is stationary on a step. You are pushing downwards and Newton says the stairs are pushing back on you with the normal force. However the normal force isn't moving so it's not doing any work on you.

In the case of a car braking without skidding the wheels are rolling. There is no relative motion between the contact patch on the tyre and the contact patch on the wheel so we are talking about static friction forces. The friction force acting on the car isn't moving so it's not doing any work on the car here. In the braking system you have relative motion between the discs and pads. It's kinetic friction and heat is produced.

In the case of a car braking with locked skidding wheels then there is relative motion between the contact patch on the tyre and the wheel, so we are talking about kinetic friction forces. These are moving as the car skids along. So in this case they do work on the car and the tyres and road gets hot. In the braking system the wheels are locked so there is no relative motion between the disk and pads. No work is being done here and the disc and pads remain cold.

In the case of a block being dragged across the floor there is relative motion between the block and floor. The friction force acting on the block is moving along with the block so work is being done on the block.

It's tempting to say static friction cannot do work on an object but it can depending on the frame of reference... Consider a package in the back of a van. Static friction between the accelerating van and the package causes the package to gain KE relative to the ground but not relative to the truck. So in one frame it's doing or transferring energy (doing work) and in the other it isn't.

poseidon721
Yes. I díd not understand it then, i hope to do it now.

By the way, you will see that Kleppner and kolenkow do compute work done by static friction on a wheel.

Nevertheless, thanks for your clarification. It was really enlightening.