# Homework Help: A doubt about frictional forces

1. Sep 24, 2010

### issacnewton

Hello

I have some doubts in the phenomona of frictional forces. I am studying from the
Serway's book. He says that direction of frictional force
is always opposite to the relative motion between the two surfaces.For example, for a block of wood
moving on the ground to the right, the force of friction exerted by the floor on the block will
be directed to the left since the relative motion of the block with respect to the ground is to the
right. This example is easy to understand. Now little more tricky example. A crate is located in the
center of a flatbed truck. The truck accelerates to the east, and the crate moves with it, not sliding at all.
Now the impending motion of the crate relative to the truck is to the west. So the direction of the friction
(force exerted by the floor of the truck on the crate) will be opposite, i.e. in the east. So here's example
where the force of friction is in the same direction as that of the motion of the truck.
Now coming to the rolling friction, I am very confused. Consider a car going on a road. The tires
of the car exert some force on the road. As a reaction to that, road exerts frictional force in the direction
of the motion of the car. Now looking at the point of contact between the road and the tire, that point
is momentarily at rest (am I right ?) with respect the road, so there is no relative motion there.
So how does road exert this frictional force on the car ?

Thanks

Newton

2. Sep 24, 2010

### Ambidext

For your first example, the truck and crate are both in the same reference frame. Friction would be thus experienced by both objects, from air resistance. If the truck accelerates at 2 m/s^2, the crate would be accelerating at that rate as well, and thus face air resistance. With reference to the truck, the crate is at rest.

As for your second example, friction goes against the acceleration of the wheels as well. However, friction works in such a way that there's a limit whereby it can be directly proportional to its corresponding driving force.

For example, a block on a table:
You push it with 1N. Friction reacting to the force will be 1N.
You then push it with 2N. Friction then becomes 2N.
At some point, friction can no longer keep up with the driving force, and thus will be capped.
If its maximum is 5N for example, when you push it with 6N, the block will be accelerated by 1N resultant force.

3. Sep 24, 2010

### JDoolin

There was no relative motion between the crate with the back of the truck either. In both cases you're using the static coefficient of friction.

$$f_{static friction} \leq F_{stat max}=\mu_s F_{Normal}$$

You should also realize that the force of friction of the tires on the road is equal and opposite the force of friction of the road on the tires.

4. Sep 24, 2010

### ehild

Friction is really tricky. Just think: it acts between two surfaces in contact and hinder relative motion of the surfaces. It is because the surfaces in contact are rough, and fit in each other like cogwheels. Static friction prevents relative motion completely; the kinetic friction slows relative motion. In case of a cart on a truck, the teeth on the rough surfaces transmit force from the truck to the cart, accelerating it together with the cart. In case of tyre and road, the wheel is rotated by the engine. Without friction, (and you can see it on an icy road) the wheels would rotate without setting the car into motion. With friction, the tyre can push the road, the road pushes back and the car starts. Or you can say that friction prevents the tyre sliding on the road, so their line of contact serves as an instantaneously fixed rotation axis. The engine exerts torque so the wheel would rotate round this instantaneous axis setting the car in motion.

ehild

5. Sep 24, 2010

### jhae2.718

For the car tire, it moves without slipping. Non-slip conditions indicate that the velocity of the center of mass of the wheel must be equal to $$r\omega$$, where r is the radius of the wheel and $$\omega$$ is the angular velocity.

Frictional forces react in order to retard motion. So the kinetic friction will act on the wheel in the direction opposite of motion. (This, by the way, is what will ultimately bring the velocity of the wheel to $$r\omega$$.)

At the point where the road is tangent to the wheel, we treat the point as if it were at rest. However, in the larger frame, the wheel is still moving forwards at a speed $$v=r\omega$$ if we assume it is perfect rolling motion. As a result, there is still a fricitional force. To maintain a constant velocity, the car has to accelerate such that the forwards acceleration is equal in magnitude to the force of friction.

6. Sep 24, 2010

### eti_07

Friction always opposes the "relative" motion between two bodies. when it comes to the cart, its motion relative to the truck is towards west. hence the friction acts opposite(towards east) and it doesn't slip as long as the force(due to acceleration) doesn't exceed the static friction. This is what happens when we stand in a train. Why are we moving along instead of staying where we are and hitting the back of the train? It is because of friction.

7. Sep 24, 2010

### PhanthomJay

With all due respect for Serway, I would say that
the direction of kinetic frictional force is always opposite to the relative motion between the two surfaces; the direction of static frictional force is always opposite to the pending relative motion between the two surfaces.

8. Sep 25, 2010

### issacnewton

Hello

Oh so many replies... sorry for answering so late..... I perfectly understood the friction in the first two cases, viz. the friction of the block on the surface and the friction of the crate on the
floor of the truck. And PhanthomJay , I know about the relation between the static frictional force and the impending motion between the two surfaces in contact.
My big doubt was about the car going on a road. Now for the car to accelerate, the car will exert a force on the road at the point of contact between the tire and the road. This force will be in opposite direction to the intended motion of the car. As a reaction to this force, the road will exert a force on the car (at the point of contact between the car and the road)
in the forward direction. As we know there is still frictional force somewhere in the picture. Is it acting in the opposite direction to the motion of the car at the point of contact.
friction is so confusing...

Thnaks

9. Sep 25, 2010

### PhanthomJay

Yes, correct.
yes, the friction force is at the point of contact of the driving tires and the road, which is less than or equal to (mu_s)N, and also on the non-driving tires, whch is equal to (mu_r)N
yes and no. Suppose you had front wheel drive. At the driving tires, as you stated above, the static friction force of the road on those tires acts forward, or else the car could not move forward. On the rear tires, there is some small rolling friction force, and the road exerts a backwards force on those tires.
Yes, it is. I probably made it more confusing.

10. Sep 25, 2010

### Quinzio

You should think of a tyre as a cogwheel.
Tyre and the road get kind of stuck one to the other.

Tyres work well because they are very elastic.
Think about train steel wheels. Trains cannot brake very hard in fact trains do have a very long path ahead when they brake. Trains starts to decelerate miles before the station.

That's because steel on steel has a low friction. You see the less the friction the less a wheel works well.

11. Sep 26, 2010

### issacnewton

hi Phanthom

The picture is becoming little clear. So yes there are driving tires and non driving tires. Like you said, at the point of contact of non driving tires, the rolling friction opposes the motion. Does it mean that the direction of rolling frictional force on the non driving tires will be opposite to the motion of the car ? Some people call this rolling friction, static friction. In what sense is it static. We are used to think of static friction, when one object is about to go in motion relative to the other object. Now this non driving tire is not steady. So I am having difficulty of thinking it as a static frictional force.

And the frictional force which is exerted by the road on the driving tire should not be called a frictional force. Because when we think of the word 'friction' we tend to think of something that opposes the motion. So I find this terminology confusing...

Final point of the posting the messages here... When I click the 'multi quote' button , it doesn't work. Also what do I do to quote from several persons who are replying to me....

Thnaks

12. Sep 26, 2010

### PhanthomJay

yes
Me too. That's why I call it rolling friction. But it is certainly not kinetic friction.
But it is friction....you don't have a problem, do you, with a crate on an accelerating truck bed, stationary with respect to the the truck, that the static friction force is acting in the direction of ts forward motion, and opposite to the direction of impending relative motion between the crate and truck bed?
I've been trying to figure that out also, for 4 years, and I still don't know.

13. Sep 26, 2010

### ehild

Try to look at this about "rolling friction":

http://webphysics.davidson.edu/faculty/dmb/PY430/Friction/rolling.html [Broken]

Last edited by a moderator: May 4, 2017
14. Sep 26, 2010

### JDoolin

The force of static friction from the road on the car is pushing forward on the tires enough to prevent the tires from skidding.

This is only happening while the car is accelerating. Once the car reaches a constant speed, you need only enough frictional force to overcome the wind resistance.

If you shove in the clutch and coast, it is the wind-resistance and friction between components of the car that cause the car to slow down.

Here's a fun game with wheels in it.

15. Sep 27, 2010

### issacnewton

Thanks everybody

PhanthomJay, so there are three kinds of frictions, static, kinetic and the rolling. I have difficulty of thinking rolling friction as same as the static friction. This website
gives the coefficients of rolling friction and the kinetic friction for different situations. For example for "Ordinary car tire on dry pavement" $$\mu_r =0.015$$ and $$\mu_k=0.8$$. I think that's the reason we use the tires in the first place, to reduce the friction.

but I think I will still maintain that for pedagogical reasons, we should just call these as forces. "Friction" does evoke the feelings that its something that opposes the motion....

I will surely look at it , echild.

JDoolin, its very funny website....will play it ....

Now let me briefly sum up all the understanding of the rolling friction so far in this discussion.

In a car, there are driving tires and the non driving tires. Driving tires exert a force on the road and as a reaction to it, the road exerts a force on the driving tire. This force helps the car to accelerate. Now for the non driving tires, the road exerts a force on these tires, whose direction is opposite to the motion of the car, at the point of contact between the roads and the tires. So when we want to draw a free body diagram for the moving car, the forward force is exerted at the driving tires and the backward force is exerted at the non driving tires and then we use Newton's second law to set up the equations of motion....

And there are frictional forces which actually help the motion....instead of opposing it...

lot of confusion is cleared I guess

Last edited by a moderator: May 4, 2017
16. Sep 27, 2010

### PhanthomJay

There are others, like fluid friction, etc., but we are focusing on those 3 types listed
You should, because they are not the same.
Racing cars use tires with high static friction coefficients on dry surfaces, to provide a greater traction force to obtain higher speeds and turn the bends without slipping occurring....if the static friction coefficient was low, the tires would slip at high speeds....if the coefficient was near 0, like on smooth ice, the car wouldn't move at all.
how about calling it a 'traction' force...but in the end, it's still friction
Unless you have all wheel or 4-wheel drive, but let's not address that
yes, created by the engine torque transferred to the driving train,
yes, the static friction force...without the road under the tires, the wheels would spin but you'd get nowhere
yes, rolling friction, which exists on the drive tires also, but small enough on those driving tires to be easily overcome by the static friction force acting on those tires,driving the car forward
yes
yes again
maybe

17. Sep 28, 2010

### issacnewton

So, we have static friction (as well as small rolling friction) at the driving tires and only
rolling friction at the non driving tires I guess..... :tongue2: that will make sense since
the net force acting on the car will be in the forward direction.....

18. Sep 28, 2010

### PhanthomJay

Yes makes sense....there are other forces acting, like air resistance and axle friction , acting in the backwards direction, that we are ignoring.

19. Sep 29, 2010

### issacnewton

Well, axle friction would be frictional torque I guess, instead of just force...

http://webphysics.davidson.edu/faculty/dmb/PY430/Friction/rolling.html [Broken]

How can we have zero friction....what is he trying to say ?

Last edited by a moderator: May 5, 2017
20. Sep 29, 2010

### ehild

There is no work done by the force of static friction. It is not a force that would change the kinetic energy. It is just a force that keeps the contact surfaces together till a force less than uN is enough for that.

If there are no dissipative forces, (air resistance or rolling resistance) no force is needed to keep up rolling without slipping on horizontal surface. So the force of static friction is 0 in this case.

ehild

21. Sep 29, 2010

### PhanthomJay

Yes, and this is why friction during translational movement on an object with tires is so confusing; Forward static friction on driving tires while accelerating, , backwards rolling friction on tires, and no static friction when moving at constant velocity. To make it more confusing, consider the case with no rolling friction, for a car moving at constant velocity when there is air resistance, say 100 N air resistance acting left on the right moving car, moving at constant velocity. Since there is no net force acting on the car at constant velocity, there must be an external 100 N force equal and opposite to the air resistance force, and that force must be provided at a contact point: by forward friction on the driving tires, which is a paradox, because there is no friction at constant velocity. It implies that a car cannot be moving at constant velocity with air resistance, but rather, it must be minutely accelerating all the time. But I'm not sure about this.

22. Sep 29, 2010

### jhae2.718

That sounds about right. When you think about it, friction really is a confusing phenomenon.

23. Sep 30, 2010

### issacnewton

that probably makes sense I guess...

Do scientists today know why this is so ? Well I found a java applet for the exact situation we are discussing here.
I found that link on This is the link to the applet I was mentioning.
http://www.phy.ntnu.edu.tw/ntnujava/index.php?topic=1727.0

But phanthomjay, there is only forward force on the driving tire shown there. You said a while ago that there is both static as well as small rolling friction on the driving tire. Or may be they have only shown the net forward force on the driving tire.

Please comment on the applet. Have they considered all the possibilities ? There are some things I am finding confusing about it though generally it agrees well with what you and others were saying.

When you turn off the power of the car, for a fraction of second , the force on the driving tire reverses direction and again it goes back to forward direction. Since the power is turned off, shouldn't there be only rolling friction on the front tire ? After the power is turned off, the direction of frictional force on the front tire is still forward. Its weird......

24. Sep 30, 2010

### PhanthomJay

ignoring air resitance and rolling friction, then per Newton 1, there is no net unbalanced force acting on an object moving in a straight line at constant speed. Can't be any static friction if there is no equal and opposite force applied, which there isn't.
yes, I believe that is correct, they show the net force forward (static less rolling) on the front tires, and rolling only backwards on the rear tires.
Seems strange to me also! First off, they show the normal force increasing on the front tires, and decreasing on the rear tires. That is not true, it's just the opposite on a level surface. For front wheel drive, the friction force creates a ccw torque about the center of mass, such that much of the normal force shifts to the rear tires. That's why most racing cars use rear wheel drive, to take advantage of the greater normal force on the rear tires and thus greater static friction force on the rear tires available for acceleration. Then comes the real kicker....as the power is turned off, the vehicle must obviously slow down and decelerate, which means the net force must act to the left...but they show the net force acting to the right. I personally would scrap that website.

25. Oct 1, 2010

### issacnewton

hi phanthomjay

i have sent an email to the author of the applet. lets see what he says. but like you confirmed my doubts, there is something wrong about that applet....

by the way, i still didn't get your point about the zero static friction when moving at constant velocity... we can't ignore the air drag and the rolling resistance.. i think that is part of the picture as well. when the car is going at constant velocity, the net force is zero, which means the forward static friction on the front tires is balanced by the rolling friction on the back tires as well as the air drag... what do you think ?

and you seem to know a lot about the friction. the usual introductory books like
serway, halliday & resnick don't have so much information about the friction. where did you learn so much......may be your background in structural engineering has something to do with it