EXPERIMENT No 5. Coefficient Of Static Friction

 

2 — Relationship between limiting friction and normal reaction; coefficient of friction

Aim

To study the relationship between limiting friction (F_l) and normal reaction (N) for a block on a horizontal surface and to determine the coefficient of limiting friction μ between the block and the surface.

Apparatus

Block (with hook), slotted weights (or weights to change normal reaction), weighing pan/string and pulley (or method to apply horizontal pulling force), spring balance or friction board with pulley, meter scale, retort stand, wooden plank or horizontal surface.

(For standard class experiments use a horizontal surface and a string attached to the block, with a spring balance to measure force at which block just begins to move — that force is limiting friction.)

Diagram:

Theory

• The limiting friction F is the maximum static friction that resists motion just before sliding begins.

• Empirically, for many surfaces F is proportional to the normal reaction N:

$$F_{}=\mu N$$

where μ is the coefficient of limiting friction (a constant for given surfaces).

• By measuring F_ for various N (by adding known weights to the block to change N), plotting F against N should produce a straight line through origin; slope = μ.

Procedure

1. Place the block on the horizontal surface. Attach a string to the block and pass it over a small frictionless pulley. Attach a spring balance in the string to apply a horizontal pull (or hang small masses to give a horizontal pull).

2. For a given normal reaction N (block weight + any added weights), gradually increase the pull until the block is just about to slide — record the force shown by the spring balance as limiting friction F.

3. Repeat the measurement for different normal reactions N (add small known weights on the block to change N), keeping the surface and block contact unchanged.

4. Record F for each N, repeat each reading 2–3 times and take average.

5. Plot F (y-axis) vs N (x-axis). Fit a straight line; slope gives μ.

Observations (sample data)

(You will replace these with your measured values. I used sample numbers to demonstrate calculation and graph.)

Trial	Normal Reaction N (N)	Limiting friction F (N)
1	10.0	6.1
2	20.0	12.3
3	30.0	18.4
4	40.0	24.8
5	50.0	30.9

Average coefficient from: μ = F/ N
Example μ values: 0.61, 0.615, 0.613, 0.62, 0.618 → mean ≈ 0.615

Graph

I generated a plot "Limiting Friction vs Normal Reaction" (scatter + best-fit line) and displayed the data table above. Replace sample data with your measurements and regenerate if you have tools to do so; slope = μ.

Result (sample)

Coefficient of limiting friction μ ≈ 0.62 (sample). Replace with result from your own measurements.

Sources of error & precautions

• Ensure pull is horizontal and there is no vertical component (tilting changes normal reaction).

• Use smooth pulley and frictionless pivot for accurate force reading.

• Repeat measurements and take averages to reduce random errors.

• Keep surface clean and consistent between trials.

• Avoid jerky pulls; increase force gradually to identify limiting friction precisely.

Conclusion

The limiting friction F is directly proportional to normal reaction N; the plot of F against N is a straight line whose slope gives the coefficient of limiting friction μ between the block and the surface.

MCQs (with answers at the end)

1. The limiting friction is the:

A. Minimum frictional force
B. Maximum frictional force before motion begins
C. Friction after the body starts moving
D. Friction when velocity is constant

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2. Limiting friction is directly proportional to:

A. Mass of the block only
B. Normal reaction
C. Surface area of contact
D. Velocity of the block

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3. The coefficient of friction (μ) is defined as:

A. μ = N / F
B. μ = F / N
C. μ = F × N
D. μ = 1 / (FN)

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4. In the experiment, the normal reaction (N) is mainly provided by:

A. Weight of the block
B. Pulling force
C. Coefficient of friction
D. Applied horizontal force

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5. The graph drawn in the experiment is:

A. Limiting friction vs angle
B. Mass vs time
C. Limiting friction vs normal reaction
D. Velocity vs time

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6. The slope of the graph between Fₗ and N gives:

A. Mass of the block
B. Normal reaction
C. Coefficient of friction
D. Limiting friction

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7. Friction is a ______ force.

A. Driving
B. Resistive
C. Conservative
D. Nuclear

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8. If limiting friction is 12 N and normal reaction is 20 N, then μ is:

A. 0.2
B. 0.4
C. 0.6
D. 0.8

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9. When the applied force just equals the limiting friction:

A. Block remains at rest
B. Block moves with constant velocity
C. Block begins to move
D. Block accelerates rapidly

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10. The relation Fₗ = μN represents a:

A. Circular relationship
B. Linear relationship
C. Parabolic relationship
D. No relationship

Answer Key

1 – B
2 – B
3 – B
4 – A
5 – C
6 – C
7 – B
8 – C
9 – C
10 – B

Quiz