Friction Explained

Friction Explained

Here i am trying to explain friction in lucid manner .This article is pretty complete . If any doubts , do post over here or in the forum.

1. It is the force that opposes relative motion between the two surfaces in contact (contact force)

2. It has been found experimentally that this force is proportional to the normal reaction force acting on the body.

f_c  N (Normal reaction)

fs= Coefficient of friction.

3. The origin of the force of friction lies in the nature of the surface of contact between the two bodies which tend to move relative to each other. At the microscopic level the surfaces of contact are not smooth. There are always some deformities. Due to these irregularities in the surface molecular forces act b/w the molecules of two surfaces and friction originates.

True a 3 kind of friction forces

1. Static friction
   
2. dynamic friction
   
3. rolling friction
   

According to Professor Richard Jones from the Department of Physics and Astronomy of the University of Sheffield

“The one item I might seriously quibble with you about is when you say that you’re interested only in static friction, not dynamic friction. What you say would certainly be true if you were talking about anything other than rubber, because static friction is usually higher than dynamic friction, so once you start to slip you keep on going. But yet again, rubber is different. Because the friction coefficient tends to increase with velocity (up to a point), and is very low for zero velocities (in fact, some researchers doubt whether there is actually a true static friction for rubber at all), I think what happens is that when you make a friction move your feet very slowly start to creep down until the friction gets to a point at which it balances the downward force. This creeping velocity is probably very small, possibly imperceptible. Yet I wonder whether those really talented climbers who have a dynamic, flowing style aren’t subconsciously aware of this and exploit it.”

Static friction: Suppose a force F acts on a body of mass m.

If the surface of contact between the body and the ground is not smooth, then frictional force comes into play. As long as the force (applied) is less than a certain limiting value (₈N) the frictional force is exactly equal and apposite to the applied force.

(Graph between force applied and frictional force)

When the applied force is just equal to the limiting value, the frictional force acting on the body is called limiting friction (maximum value of static friction). Thus, static friction acts whenever there is a tendency of relative motion between two bodies (not actually moving relative to one another).

Dynamic Friction: Whenever two bodies are actually in a state of motion relative to each other, then the force of friction that comes into picture is the force of dynamic friction. It has been found experimentally that this force is also proportional to the force of normal reaction but has its value a little less than that of limiting friction. Unlike static friction the force

of dynamic friction remains constant throughout the motion of bodies.

Besides the two kinds of frictions discussed above another kind of friction known as rolling friction is also there. It will be discussed in details in the chapter concerning rotational mechanics.

Problem (1):

Q. The co-efficient of static friction

B/w the two blocks shown in figure is k & base is frictionless what is the max. horizontal force that can be applied to it (bigger block) so that blocks move together ?

Sol:
analysis: Since both block move together both will have acclⁿ a Let, the force acting on the bigger block is

Now suppose there were no friction between the blocks of masses m and M, then as force F acts on the bigger block towards right, then as observed by an observer on the ground the bigger block moves in the direction of the applied force. Now, since no external force is acting on the smaller block (in the absence of friction), according to Newton’s first law, the block will remains stationary as seen by the observer on the ground.

Thus, in absence of friction the smaller block will tend to remain stationary w.r.t the ground and move towards left w.r.t the bigger black.

Since, friction is the force which tends to oppose the relative motion between two bodies it will act towards right on the smaller black and towards left on the bigger block.

Since, are have to calculate the maximum horizontal force, the frictional force opposing motion will be that of limiting friction.

…(1)                 …(4)

…(2)                 …(5)

Problem : (2)

The horizontal surface of the bigger block is smooth & the co-efficient of friction b/w the blocks is . What the max. & min. force F can be applied so that smaller block remains at rest with respect to the bigger block?

In the above problem since the two smaller masses are connected by a string the mass hanging from the pulley will tend to move down under the action of gravity. Thus it will apply a force of tension on the other block and in the absence of any force the mass placed on the bigger block will tend to move towards right.

Case-I: Now suppose the force starts acting on the bigger lock towards right. In the absence of any friction for an observer in an inertial frame on the ground, the bigger block will tend to move in the direction of force and due to tension in the thread smaller mass m placed on it will also tend to move toward right.

Thus, frictional force will come into play which will tend to oppose this relative motion and will act on the smaller block towards left.

Now, suppose F acts on the bigger block which not only causes the bigger block to move but also causes the normal reaction force on the mass hanging to increase so that the frictional force b/w hanging mass and bigger block will also increase causing it to remain stationary (also causing the mass on the block to remain at rest).

Case-II : Now, suppose the force F is increased, then a stage will come when the tendency of motion of the block placed on the bigger block will be towards left opposite to the tension T, then the force of friction will start acting towards right on the block m now, if F exceeds a certain value F_max then the resultant force on m will move it towards left and will overcome the frictional force.

This problem can be easily analyzed placing the observer on the bigger block as the condition of the problem will be such that the block should remain stationary to this observer and thus the resultant of force acting on it and the mass hanging can be equated to O to obtain the required result. But in that case pseudo force will have to be taken into account due to of M.

analysis :

Case (1) when blocks tend to move in forward dirⁿ

Free body diagram

(1)

eqⁿ of motion :

…(1)

…(2)

Case-(2) : When the block tend to move in back ward direction.

This will be the case when F will be max. & the block will tend to move to in the back ward direction.

eqⁿ of motion :

…(1)

…(2)

…(3)

…(4)

(3) + (1)

Suppose F is applied to the system in above figure

Then

The a u/ⁿ of system will be

Problem (3): the figure below shows a small block of mass m kept at the left end of the larger block of mass M and length L. the system can slide on a horizontal road. The system is started towards right with an initial velocity v. the friction co-efficient between the road and the bigger block is as shown and that between the smaller and bigger block is half of that. Find the time elapsed before the smaller block separates from the bigger block.

To analyze the above problem first let’s determine the direction of frictional forces acting between the two surfaces of contact. Since the bigger block is in motion along the right, therefore the frictional force due to its relative motion w.r.t. the ground will act towards the lect.

Again, since the system comprising both the smaller block and the bigger block is given the initial velocity v(and not the bigger block alone), therefore the motion of the smaller mass w.r.t. the bigger mass should not be there in the absence of any frictional force.

Now, since, the coefficient of friction (dynamic friction in this case) is different b/w the two surfaces, the bigger block is more retarded due to friction in comparison to the smaller block and thus it moves towards right relative to the bigger block.

Solution:

From the laws of motion    

In A the –ve sign shows that the block will move in the opposite dirⁿ from the dirⁿ we considered in the solution.

Problem (4): the friction co-efficient between the board and the floor is as shown. Find the maximum force that the man can exert on the rope so that the board does not slip on the floor.

In the above problem suppose the man exerts a force F on the rope, then this force will act as tension in the rope. Since, the rope is taken to be inextensible, therefore the relative motion of the block w.r.t. the ground is in its direction and thus frictional force will act towards the left to oppose the relative motion of the block. If the tension exceeds the value of limiting friction, the block will start slipping on the Floor.

…(1)

…(2)

…(3)

For the condition of not sliding

a = 0

F = f_s

F = R