What is the Coefficient of Friction? 

Friction is the force that opposes relative motion between two objects which are in contact with each other. The coefficient of friction is the ratio of the resistive force of friction to the perpendicular force (normal reaction) pushing the objects.

It is denoted by the Greek letter mu (μ).

Mathematically, μ = F/N

(F = Frictional force , N = normal reaction)

The coefficient of friction is a dimensionless quantity.

Types of Coefficient of Friction

Coefficient of friction is of two types. One is kinetic (a.k.a dynamic or sliding friction coefficient), which means that the objects in contact are already in motion relative to each other, the other is static( a.k.a starting friction coefficient), which means the objects are at rest with respect to each other.

How to Calculate Coefficient of Friction?

Coefficient of friction can be calculated by using the formula

μ = F/N  where, F = Frictional force , N = normal reaction

For calculating the coefficient of static friction (μ s), we use

μ s= FLN here, FL= Limiting friction or maximum value of static friction, N = Normal reaction.

While for calculating the coefficient of kinetic friction (μ k), we use

μ k= FkN here, Fk= kinetic friction, N = Normal reaction.

Usually, μ s>μ k.

Coefficient of Friction Formula

μ = F/N  where, F = Frictional force , N = normal reaction

Coefficient of Friction Experiment

Experiment Title – Finding Coefficient of Friction

Experiment Description – The concept of coefficient of friction may be confusing, but don’t worry. Come and understand what the coefficient of friction is and how it is calculated through this experiment.

Aim of Experiment – To study the relationship between the force of limiting friction and normal reaction and find the coefficient of friction between the surface of a moving block and that of a horizontal surface.

Material Required – A wooden block with a hook, a horizontal plane with a laminated tabletop, a frictionless pulley, spirit level, scale, pan, string, spring balance, weight box of different masses

Procedure –

1. Observe the spring balance and find its range and least count.
2. Using the spring balance, measure the mass (M) of the given wooden block with hooks on its sides and the scale pan (m).
3. Take the laminated tabletop and place it horizontally. Ensure that the tabletop surface is horizontal using a spirit level, and also take care to clean and dry the top surface. 
4. Fix a frictionless pulley on the edge of the tabletop, as shown in the figure below. Lubricate the pulley if necessary.

5. Tie one end of a string of appropriate length, according to the size and height of the table, to a scale pan and its other end to the hook of the wooden block.
6. Placing the wooden block on the horizontal plane, pass the string over the pulley as shown in the figure above. Make sure that the portion of the string between the pulley and the wooden block is horizontal by adjusting the height of the pulley to the level of the hook of the block.
7. Place any mass (q) on the scale pan. Tap the tabletop gently with your finger to see if the block starts moving.
8. Keep increasing the mass (q) on the pan until the wooden block just starts moving. Note the total mass on the scale pan in the observation table. 
9. Place an additional known mass (p) on the wooden block and the mass (q’) on the scale pan so that the wooden block with mass p just begins to slide. Record the values of p’ and q’ in the observation table. 
10. Repeat the above step for three or four more values of p and note the corresponding values of q in the observation table. At least five sets of observations are needed for plotting a graph between F_L and R. 

Graph: Taking the limiting friction F_L on the Y-axis and the normal force R on the X-axis, plot a graph between the limiting friction (F_L) and normal force (R) between the wooden block and the horizontal surface. Join all the points marked with a straight line, as shown in the figure below.

The straight line may not pass through all the points, a few of which may lie on either side of it. Extend the straight line backwards to see if it passes through the origin. The slope of this straight line gives the coefficient of limiting friction (μ_L) between the wooden block and the horizontal surface. As shown in the figure above, choose two points, A and B, that are far apart from each other on the straight line to find its slope. Draw two lines, one parallel to the X-axis through point A and the other parallel to the Y-axis through point B. Let the intersection of these two lines be point Z. The slope μ_L of the straight line AB would be

                                        L = FLR = BZAZ

Precautions – 

1. Keep the surface of the tabletop horizontal and dust-free.
2. Keep the string connecting the wooden block and the pulley horizontal.
3. Oil the pulley to reduce the friction.
4. Tap the tabletop gently.

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