Relationship Between Force of Limiting Friction and Normal Reaction

The force which is opposing the object will arise as a reaction to the applied force and acts in the opposite direction when a body makes an attempt to slide over another body.

We know that when a frictional force opposes an object, there arises a reaction to the applied force that acts in the opposite direction during the time when a body makes a try to slide over another body.

Generally, a frictional force is categorized into four types, viz: Static Friction, sliding friction, rolling friction, and fluid friction, as we can understand the significance of each by their first name. However, there’s another new term, i.e., limiting friction. It seems to be something different, but what does it stand for and what is its application?

Also, how does it vary from other terms mentioned above and relate to the normal reaction?

Answers to all queries mentioned above are available on this page with illustrating differences and examples on the same. 

Force of Limiting Friction Definition

Static friction exists when two objects touch each other at rest. This friction has a limiting value which is called limiting friction, and which is equal to the least force required to move the body from rest. When the external force F is increased, it makes the body just on the verge of moving. The force of friction is maximum at this stage, and that is called limiting friction.

The limiting frictional force is called the coefficient of static friction, which is found experimentally. The coefficient of friction is a dimensionless constant, but it depends on the nature of surfaces in contact.

How Force of Limiting Friction Relates with Normal Reaction?

It is observed that when the total weight pulled rises, the force of limiting friction also increases. However, this increase remains in direct proportion. 

(Image will be uploaded soon)           

The graph drawn above shows that limiting friction F is directly proportional to the normal reaction R. Hence, this is in agreement with the law of limiting friction.

Now, let us perform an experiment to derive the value of the coefficient of static friction to describe the relationship of the limiting frictional force and normal reaction. 

Experiment For Finding The Coefficient Of Friction to Determine Coefficient of Static Friction 

Objective

The aim of the study is to identify the relationship between the force of limiting friction and the normal reaction and to find the coefficient of friction between a block and a horizontal surface.

Apparatus Required:

• A Wooden block

• A 50g or 20g weights

• A horizontal plane fitted with a frictionless pulley at one end

• A pan

• A spring balance

• A thread

• A spirit level

Theory:

We know that, friction between two surfaces when the bodies are sliding over them is known as sliding friction. It is also called kinetic friction.

The least force required to make a body slide over the surface is known as the force of the sliding friction.

Force of friction,

F ∝ N

On removing the sign of proportionality constant, we get:

F= μ N

Where,

μ is the coefficient of friction

N is the normal reaction

F is the force of sliding

At the equilibrium, the net force should be zero

F = P + p 

R = W + w

Study for the force of sliding friction

Procedure:

1. The pulley should be free of friction, and the tabletop should be clean.

2. The block should be passed on to the pulley by tieing one end of the thread on the hook of the wooden block.

3. The weight of the pan should be found.

4. The pan should be tied to the free end of the thread and left hanging vertically.

5. To pull the block easily, some weights should be put on the pan.

6. The tabletop should be tapped, to make the block slide, by adding the weights little by little, continue the tapping.

7. The total weights of the pan in the observation table should be recorded.

8. Steps 8, and 9, should be repeated, by adding one 50g or 20g weight on the wooden block, and repeating steps 8, 9, and 10 six times.

Observations:

1. The weight of the wooden block (w) should be recorded in  g wt.

2. The weight of the pan (P) should be recorded in g wt.

3. The weight on the wooden block (w) should be recorded in g wt.

4. The weight being pulled (W+w) should be recorded in g wt.

5. Weight on the pan (p) should be recorded in g wt.

6. The total weight being pulled (block and weights) (P+p) should be recorded in g wt, which is the limiting friction (F) in  g wt.

Calculations of our Experiment:

1. The value of the force of sliding friction is being given by the total weight.

2. The normal reaction R should be given by the total weights being pulled on the horizontal surface. 

3. A graph between normal reaction R and limiting friction F should be plotted, taking R along the x-axis and F along the y-axis.

As shown below the graph comes to be a straight line:

(Image will be uploaded soon)

Here, slope of the graph tan  is the coefficient of static friction, whose formula is as follows:

\[tan \theta\] =  \[\frac {F}{R}\]

\[\mu \] =  \[\frac {F}{R}\]

Results:

In the above graph between R and F, we have R as 300 and F as 75. Now, using our above formula:

                  =\[\frac {F}{R}\]=\[\frac {75}{300}\]  

We get μ = 0.25  

Fun Facts

1. Friction is a force that opposes when two objects slide against each other and is a contact force like the normal force. Friction acts in the flat surface direction of an object, while the normal force acts perpendicular to the flat surface.

2. It is found that the total weight pulled, and the force of limiting friction both increase simultaneously.

3. The thread part between block and pulley is kept horizontal for the equal distribution of the total weight of pan and weights.

4. The roads become slippery after rains, due to the reduction of friction between feet and the road, for the thin layer of rainwater between them.

5. The surface of the brake is flat because, when the brake is pressed, it gets pushed from hydraulic pistons and the surface of the brake rotor. So the surface should be flat since it is getting pushed from both sides.