# 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.

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.

### Experiment For Finding The Coefficient Of 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:

1. A Wooden block

2. A 50g or 20g weights

3. A horizontal plane fitted with a frictionless pulley at one end

4. A pan

5. A spring balance

7. A spirit level

### Theory:

The 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 ∝ RF

F= μR

Where,

μ is the coefficient of friction

R 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

Diagram:

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 table top 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 repeat 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:

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 x-axis and F along the y-axis.

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

The graph between R and F

### Result:

1. From the graph, it's clear that the limiting friction F is directly proportional to the normal reaction R. It's an agreement with laws of limiting friction.

2. The constant ratio is also called the coefficient of friction (). It can be calculated by finding the slope of the graph.

In ABC,

Slope of the straight line AB = tan$\theta$ = $\frac{BC}{AC}$ = $\frac{F}{R}$     --(1)

But, F= μR

$\frac{F}{R}$ = μ                               --(2)

μ can be calculated from equation (1) and (2)

### 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.