# Work done by friction

1. ### iitjee10

57
Waht is the work done by friction when a man is walking? zero or nonzero?
[ friction is not causing the displacement of point of contact.....or is it?]

I was analysing the work done by friction and i seem to get conflicting answers.
If we consider the displacement of point of contact, it is zero, hence work done by friction must be zero.
However if we use Work-Energy theorem, as the man acquires some velocity, so some amount of positive work is done. As the only EXTERNAL force which can do work is friction, what is the work done by friction? (zero of positive)?

### Staff: Mentor

Unless the man's shoes slip, friction does no work on the man when he walks. Nonetheless, Newton's laws still apply--that's where the so-called "work"-energy theorem comes from. In order for the man to accelerate, there must be an external force on him, which is friction. But that friction does no real work, thus does not provide energy. (The energy comes from his muscles, not from the ground.)

3. ### kyiydnlm

34
Doc Al is right. Friction does not provide energy; muscles do.
Friction causes velocity change of this man is because of momentum.
fdt = d(mv), f is friction

4. ### RestlessMind

174
The man produces the energy from his muscles like these guys said. The friction between his shoe and the ground is a place to anchor his foot, really...

5. ### pgardn

637
So I guess we have to look at more than mechanical energy when analyzing this situation. What you really appear to have is chemical energy (from the muscles in his body, thru respiraton) converted to Kinetic Energy.

6. ### iitjee10

57
Thanks a lot everyone.

7. ### sganesh88

288
Ok. The actual energy comes from his muscles; Now the increase in KE should be equal to the friction force multiplied by the slipping distance right? But more slipping also means more energy loss in the form of heat. Does that imply that the more energy we lose while walking, the higher KE and speed we gain? or am i missing something here?

### Staff: Mentor

There's no slipping in this case, so no energy is lost to friction. From Newton's 2nd law, the change in KE will equal the force applied (static friction) times the displacement of the center of mass (not the point of contact, which doesn't move). (That's the so-called "work"-energy theorem, although no real work is done.)

9. ### sganesh88

288
Thanks Doc! So it's the motion of COM that matters. I thought the point of application should move for the force to do work. This also helped clear my doubt regarding the role of static friction propelling vehicles.

### Staff: Mentor

The motion of the COM matters when applying Newton's 2nd law.
That's right. Since the point of application doesn't move in this case, no work is done by friction.
Good.

Another example to ponder. A man crouches down, then jumps into the air. The ground exerts an upward force on him during his jump, but since the point of application doesn't move, the ground does no work on him. (His muscles provide the energy.) But you can still apply Newton's laws.

11. ### Naty1

NO. Chemical energy consumed by the body in biological processes is NOT equal to the KE produced. Think about pushing just as hard as you can against a wall that does not move. Assuming your feet don't slip and you don't move the wall, virtually no work is done...unless you want to count a tiny bit of compression heat on surfaces which is negligible.

Another way to realize that such "chemical" energy does NOT equal KE is is to recognize that such biological energy is consumed in large part by keeping the individual warm, erect against gravity, allowing the individual to digest food, breath,think...etc. If I recall correctly, human brain consumes something on the order of 20% of the bodies energy!!

### Staff: Mentor

I'm not sure I understand the point you are making here. Certainly the KE produced is (ultimately) transformed chemical energy. Of course, the chemical energy consumed is not equal to the KE produced (it's much greater), but I don't think anyone was making that claim.
That's true.

13. ### dE_logics

735
Considering friction between his shoes and ground, if there is no slip, no work is done cause of friction.

Friction does not do work...work is done cause of friction (actually it's the process of convention of motion to other forms of energy).

Friction just provides a normal reaction.

Yes, law of conservation of momentum states that no motion can be made unless there's action from an external force...this external force is the normal reaction provided by friction.

First you apply a force on the ground, and the ground reacts through friction giving you a net velocity.

14. ### sganesh88

288
I am confused again. Pardon and help me. :(
Say where i have gone wrong.
1. External force has to do work on the body to increase its KE.
2. Static friction is the only net force on the human body while walking. (neglect the slight vertical motions of the COM)
3. So static friction should do work.

But you're saying
What significance does the value of friction force multiplied by the displacement of COM that you mentioned in the previous post have?

I have another hypothetical situation that sort of explains this(similar to the crouching and jumping scenario Doc Al mentioned) Imagine two hemispheres joined together loosely; the upper and lower hemispheres are connected by long strings. So initially the strings are flaccid. Now the conjoined hemispheres- are placed on a surface with a hemispherical cup to accommodate the lower hemisphere. Now an explosive placed inside the sphere is triggered. The lower part cannot move initially and the upper part alone shoots up wholly due to the internal force of the explosive. As for the application of newton's laws goes, the system's COM accelerates due to the normal force from the surface. Since work done requires the movement of the point of application, it is done only by the internal force increasing the KE of the upper hemisphere. Then the moving upper hemisphere pulls the lower one through the string which is also an internal force. This is what happens while walking too, i think.
So work needn't be done by the external force. 1 is wrong then. Friction, as de_logics said, acts like a bridge to convert the system's energy from one form to the other; allowing internal forces to do work on one part of the system while preventing it from doing the same on the other. This is the critical point.
Sorry for the long post but i thought i should explain what i think. It would be helpful to someone who is facing a similar doubt i think.

### Staff: Mentor

No, an external force must act on the body, but not necessarily do work. (Where work is defined in the First Law of Thermo sense: a force acting through a displacement of the point of application.)
Multiplying the applied force (friction) times the displacement of the COM gives the change in KE of the body. (This is a consequence of Newton's laws, not conservation of energy.) While that looks like a work term (F*Distance), it's properly called pseudowork. Real work is force*displacement of the point of application, which is zero in this case. In many physics 101 problems the distinction doesn't matter, since you can often treat bodies as if they were point masses.

If you studied the walking man as a system interacting with its environment, you'd see that while an external force acts, since it does no real work it transfers no energy into the system. Make sense?

16. ### dE_logics

735
A force should also produce displacement to do work...static friction poses no displacements...so no work is done.

All static friction does is 'redirect' the force so as to move the body.

17. ### sganesh88

288
I should try deriving this.
And i wasn't aware of something called pseudo-work. Thanks for helping out. :)
Do tell whether i was right in the two-hemispheres scenario mentioned in the latter part of my post..

18. ### vin300

533
Consider this:A rigid body collides normally with a rigid surface
The momentum of the system at every instant must be conserved, so when the two are in contact in the rest frame of the observer, there must be something with a momentum. The surface or the body still has a momentum, so saying the displacement of the point of contact is zero is an approximation, it actually moves,if the body recoils with no damage at all, it proves that nothing is really rigid.

Last edited: Aug 25, 2009
19. ### RohansK

37
The friction between the ground and the human foot/shoe sole actually holds the foot or keeps it grounded firmly. This is kind of an interlocking between the two surfaces which facilitate the muscles to exert the force to actually push your body forward.

Had the friction been overcome you would keep on slipping on the ground and forward motion wouldnt be possible. ( just as the case of a car tyre slipping on a mucky road)

So the frictional force is at the base point of contact and this point of contact does not move. So the friction does not do any work. It is the muscular energy that does the work of pushing your body forward.

20. ### vin300

533
How is this a reply to my post?

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