Friction & normal force lab report

1. Title and aim

The laws of friction: Determination of the coefficient of sliding friction. Investigate Amontons–Coulomb laws of friction and determine the coefficient of kinetic friction μ by linear regression of friction force against normal load.

2. Abstract

Five observations were generated from the ideal teaching model over the settings listed below. A straight-line fit gave an estimate of coefficient of kinetic friction μ of 0.3500 , differing by 0.000% from the model value. The reported scatter comes from scale rounding and any stated model approximation, not measured laboratory noise.

3. Apparatus and fixed settings

• Precision spring dynamometer: Applies and measures the horizontal pulling force required to maintain steady slider motion with 0.02 N resolution.
• Weighted contact slider block: Provides uniform planar contact surfaces with captive tray for holding calibrated slotted weights.
• Horizontal friction bed track: Provides a rigid, level, polished guiding surface for slider travel.
• Set of calibrated slotted weights: Allows normal compressive force N to be varied systematically from 1.0 N to 14.0 N.
• Contact surfaces: Polished maple slider block on smooth horizontal maple test track.
• Ambient conditions: 20.0 °C, relative humidity 45%, clean dust-free dry surfaces.
• Dynamometer: Precision tubular spring balance with 0.02 N scale resolution.
• Motion regime: Uniform steady velocity (v ≈ 0.05 m/s) to ensure kinetic regime without inertial acceleration.

4. Theory and graph choice

The macroscopic resistive force between two solid contact surfaces in relative sliding motion is governed by Amontons’ laws of friction: the frictional force F_f is directly proportional to the normal compressive load N and is largely independent of the apparent macroscopic contact area and sliding speed at low velocities: F_f = μN. The dimensionless coefficient of kinetic friction μ characterizes the microscopic surface asperities and adhesion between the contact materials.

The calculation fits y = mx + b in SI units. The graph may display scaled axes for readability; those display factors are removed before calculating the physical result. The gradient has units dimensionless.

5. Method

1. Hold the spring balance horizontally on the bench, tap gently to relieve internal spring friction, and record any zero-point offset.
2. Verify with a spirit level that the track is strictly horizontal, and wipe both the slider base and track bed with clean lint-free cloth.
3. Load the slider tray with slotted weights to establish the desired total normal force N (slider tare weight plus added load).
4. Connect the spring balance hook to the slider eyelet parallel to the bench and pull steadily until the slider transitions from static grip to uniform constant sliding.
5. Note the force reading on the dynamometer while the slider is in steady, non-accelerating motion across the central test span.
6. Repeat the observation across all five independent normal loads from 2.0 N to 10.0 N to assemble the linear regression dataset.

6. Observations and calculation table

All observations use fixed model settings. Values are rounded only at the instrument reading stage; further calculations use full precision. Repeated physical trials are not claimed.

Download the sample observations (CSV) ↓

7. Worked calculation for one observation

8. Graph, gradient and final calculation

Dots show the sample observations. The line is the ordinary least-squares fit.

9. Uncertainty and comparison

Percentage difference = |estimate − model value| / |model value| × 100 = 0.0000%. Percentage difference is not experimental uncertainty.

For n = 5 observations, Σresidual² = 7.8886e-31; s² = Σresidual²/(n − 2). Gradient standard error = √[s²/Σ(x − x̄)²] = 8.1079e-17. Intercept standard error = √[s²(1/n + x̄²/Σ(x − x̄)²)] = 5.3782e-16.

Propagating only the relevant fit coefficient gives a fit-only standard error of 8.1079e-17 . This is a one-standard-error quantity under the regression assumptions. Deterministic rounded model data do not supply a complete physical uncertainty budget.

Local variations in microscopic surface roughness, stick-slip velocity fluctuations, track leveling error, and dynamometer spring calibration contribute uncertainty. Pulling at a slight angle alters the effective normal force. The linear regression standard error reflects scatter in steady-state sliding readings but excludes systematic track misalignment.

10. Result and discussion

The observations follow the stated model relationship. Check whether the intercept and residual pattern suggest a systematic offset or a missing approximation. Agreement with the model does not independently verify its input constants.

11. Precautions and limitations

• Determine the dynamometer zero offset in the horizontal position before collecting friction readings.
• Ensure the friction bed is wiped completely clean of dust, grit, or oil films that would alter the interfacial friction.
• Keep the pulling string strictly parallel to the bed surface to ensure the normal force equals the total gravitational weight.
• Record the dynamometer reading only when the slider is moving at a steady, uniform velocity without acceleration.

The simulation assumes dry Coulomb friction between homogeneous rigid surfaces without thermal softening, surface wear degradation, or stick-slip resonance. Observations reflect polished wood-on-wood contact (reference μ = 0.350) with standard dynamometer reading resolution of 0.02 N.

12. Conclusion

The worked example illustrates how to obtain coefficient of kinetic friction μ from measurements, graph variables and a fitted coefficient. The estimate is 0.3500 . A real experiment must additionally evaluate the apparatus-specific uncertainties and corrections described above.