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Home / Physics / Understanding the Relationship between Force of Limiting Friction and Normal Reaction

Understanding the Relationship between Force of Limiting Friction and Normal Reaction

Last Updated on Jan 22, 2025
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Friction, a common force between two bodies in contact, can be static in nature. The maximum value static friction can reach before the body starts moving is called limiting friction. When the applied force surpasses the limiting friction, the body starts moving. This article explores the relationship between the force of limiting friction and normal reaction. It also provides a guide on how to find the coefficient of friction between a block and a flat surface.

Table of Contents:

Purpose

The aim of this study is to investigate the relationship between the force of limiting friction and normal reaction and to determine the coefficient of friction between a block and a flat surface.

Required Materials
  1. A wooden block
  2. Weights of 50g or 20g
  3. A flat plane with a frictionless pulley on one end
  4. A pan
  5. A spring balance
  6. A thread
  7. A spirit level

Theoretical Framework

What is Sliding Friction?

Sliding friction is the resistance encountered when two bodies slide over each other. It is also referred to as kinetic friction. Here are some different instances of sliding friction:

  • Rubbing two sticks together to start a fire.
  • A sled gliding over snow.
  • A book sliding off a table.

What is the Force of Sliding Friction?

The force of sliding friction is the minimum force necessary to make a body slide over a surface.

The force of friction,

Where,

  • is the coefficient of friction
  • R is the normal reaction
  • F is the force of sliding

At equilibrium,

F = P + p

R = W + w

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Illustration

Methodology
  1. Ensure the pulley is frictionless and the tabletop is clean.
  2. Before placing the block on the tabletop, weigh the block.
  3. Tie one end of the thread to the hook of the wooden block and pass it over the pulley.
  4. Determine the weight of the pan.
  5. Tie the pan to the free end of the thread so it hangs vertically.
  6. Place some weights on the pan to facilitate the movement of the block.
  7. Start tapping the tabletop to initiate the block's slide.
  8. Continue tapping and gradually add weights.
  9. Record the total weights in the pan in the observation table.
  10. Repeat steps 8 and 9, this time adding a 50g or 20g weight to the wooden block.
  11. Repeat steps 8, 9, and 10 six times, each time increasing the weight by 50g or 20g.
  12. Record the observations as indicated below.

Observations

Weight of wooden block, W = ……g wt

Weight of pan, P = ……g wt

Table for additional weights:

Sl.no Weights on a wooden block (w) in g wt The total weight being pulled (W+w)= Normal reaction in g wt Weight on the pan (p) in g wt Total weight pulling the block and weights (P+p)=limiting friction (F) in g wt
1.        
2.        
3.        
4.        

Calculations

The total weight pulling the block and weights represents the force of sliding friction.

On a flat surface, the total weights being pulled give the normal reaction R. The total weight pulling these weights gives the dynamic friction F.

Draw a graph between normal reaction R and limiting friction F, taking R on the x-axis and F on the y-axis.

The resulting graph is a straight line as illustrated below:

Results

The results show that as the total weight pulled increases, the force of limiting friction also increases proportionally.

The graph demonstrates that limiting friction F is directly proportional to the normal reaction R. This is in accordance with the law of limiting friction.

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

In ΔABC,

Slope of straight line AB = tan Ө =

tan Ө =

………..(1)

 

But,

………………(2)

 

From equation (1) and (2),

Precautions
  1. Ensure the tabletop is level.
  2. The thread between the block and the pulley should be level.
  3. Add weight to the pan in small increments to prevent oscillation or rotation.
  4. Gently tap the tabletop.
  5. Use a frictionless pulley.

Potential Errors
  1. The tabletop may not be level.
  2. The thread between the block and the pulley may not be level.
  3. A frictionless pulley may not have been used.

 

 

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Frequently Asked Questions

It is kept horizontal for the equal distribution of the total weight of pan and weights.

By using a frictionless pulley the overall effective value can be reduced.

Friction between the feet and road reduces when there is a thin layer of rainwater between them. So the roads become slippery after rains.

The surface of the brake are flat because when the brake is pressed, it gets pushed from hydraulic pistons and the surface of the brake rotor. Since it is getting pushed from both sides, friction is created and so the surface should be flat.

Examples for sliding friction are: Hands are rubbed together, to produce heat, Skis sliding against the snow, Sliding of a block across the floor.
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