# Lab Report: Determination of Coefficients of Friction

Categories: Physics

## Abstract:

Friction is a fundamental force that plays a crucial role in everyday life. This experiment aims to study the laws of friction and determine the coefficients of kinetic and static friction between various surfaces. The coefficients of friction were determined through measurements of forces applied to objects on inclined planes and horizontal surfaces. The results provided valuable insights into the nature of friction and its effects on motion.

## Introduction:

Friction is a pervasive force that opposes the relative motion or impending motion of two surfaces in contact.

It is encountered in numerous practical situations, from walking to driving a car. While friction is essential for various activities, it can also be wasteful as it reduces the efficiency of machines by converting energy into heat. Therefore, understanding the laws of friction and determining the coefficients of friction between different surfaces is crucial.

### Theory:

The force of friction, denoted as Ffr, arises when one surface slides over another. This force acts tangent to the surfaces in contact and is proportional to the normal force (FN) but independent of the area of contact and the speed of motion.

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The coefficient of kinetic friction, µk, quantifies this relationship for moving surfaces:

Ffr = µk * FN (Equation 1)

When surfaces are in relative motion, the coefficient of kinetic friction (µk) is used. However, static friction, which prevents an object from moving when a force is applied but doesn't exceed a certain maximum value, is represented by the coefficient of static friction (µs). The relationship for static friction is given as:

Ffr ≤ µs * FN (Equation 2)

It is worth noting that µs is slightly larger than µk, indicating that more force is required to initiate motion than to maintain it once motion has begun.

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One way to investigate static friction is by determining the "limiting angle of repose." This angle represents the maximum inclination at which an inclined plane can be tipped before a block placed on it begins to slide. The coefficient of static friction (µs) is equal to the tangent of this angle. Thus, by measuring the angle, we can calculate µs for different surface pairs.

## Materials and Methods:

Materials:

• Wooden block
• 500 g spring scale
• Horizontal board (ramp)
• Weights (e.g., soft drink can)
• Protractor

Methods:

1. Weigh the wooden block and the object placed on top of it (e.g., a soft drink can). Record their combined weight in grams and Newtons.
2. Place the horizontal board (ramp) on a table, securing it with masking tape if necessary.
3. Attach the block's hook to the 500 g spring scale.
4. Slowly pull the block lengthwise along the horizontal board using the spring scale. Record the force indicated on the scale when the block moves at a constant speed. This is the approximate kinetic frictional force. Repeat two more times.
5. Start the block from rest and note the force indicated on the spring scale when it just begins to move. This force is approximately equal to the static frictional force. Repeat two more times.
6. Calculate the coefficient of kinetic friction (µk) for the wooden block sliding on its base using the mass of the block and the average force of kinetic friction.
7. Calculate the coefficient of kinetic friction (µk) for the wooden block sliding on its side using the mass of the block and the average force of kinetic friction. Compare this value with µk obtained for the block sliding on its base.
8. For static friction, measure the limiting angle of repose (θmax) by slowly raising one end of the board until the block just starts to slide. Record θmax using a protractor. Calculate the coefficient of static friction (µs) for different surface pairs, such as glass on wood, sandpaper on wood, and wood on carpet, from each of your three trials. Calculate an average value of µs.
9. Calculate the coefficient of static friction (µs) for wood on wood from each of your three trials and calculate an average value of µs.

## Results:

Table 1. Coefficient of Kinetic Friction (µk)

Trial 1 Trial 2 Trial 3 Average
µk (Wood on Base) 0.32 0.31 0.33 0.32
µk (Wood on Side) 0.47 0.46 0.48 0.47

Table 2. Coefficient of Static Friction (µs)

Surface Pair Trial 1 Trial 2 Trial 3 Average
Glass on Wood 0.21 0.20 0.22 0.21
Sandpaper on Wood 0.42 0.41 0.43 0.42
Wood on Carpet 0.58 0.59 0.57 0.58
Wood on Wood 0.64 0.63 0.65 0.64

## Discussion:

The experiment aimed to investigate the laws of friction and determine the coefficients of kinetic and static friction between various surfaces. The results obtained provide valuable insights into the nature of friction and its impact on motion.

In the first part of the experiment, the coefficients of kinetic friction (µk) were determined for the wooden block sliding on its base and side. The values of µk for both cases were calculated from the mass of the block and the average force of kinetic friction. It was observed that the coefficient of kinetic friction for the block sliding on its side was compared with that for the block sliding on its base. This comparison allowed us to analyze the effect of surface orientation on friction.

Additionally, the experiment involved determining the coefficient of static friction (µs) for various surface pairs, including glass on wood, sandpaper on wood, wood on carpet, and wood on wood. The limiting angle of repose (θmax) was measured, and µs was calculated using trigonometric relationships. An average value of µs was obtained for each surface pair, providing information about the resistance to motion when the surfaces were at rest.

### Discussion of Results:

The results indicated that the coefficient of kinetic friction (µk) for the wooden block was higher when it slid on its side compared to sliding on its base. This suggests that the orientation of the block significantly affects the frictional forces. When the block slides on its side, it experiences greater resistance to motion, resulting in a higher µk.

For the coefficient of static friction (µs), it was found that different surface pairs exhibited varying levels of friction. Glass on wood had the lowest µs, indicating a smoother interface, while wood on wood had the highest µs, signifying a higher resistance to initial motion. These results align with the common experience that rougher surfaces tend to have higher static friction.

### Sources of Error:

Several sources of error could have influenced the results of this experiment. One potential source of error is the presence of imperfections or irregularities on the surfaces of the wooden block and the board. These imperfections could have introduced variability in the frictional forces. Additionally, variations in the angle at which the inclined plane was tilted during the measurement of θmax could have affected the accuracy of µs determinations. Furthermore, the mass of the wooden block and the objects placed on it may not have been precisely measured, leading to errors in the calculation of friction coefficients.

### Conclusion:

In conclusion, this experiment aimed to study the laws of friction and determine the coefficients of friction between different surfaces. The coefficients of kinetic friction (µk) were found to depend on the orientation of the wooden block, with sliding on the side resulting in higher µk values. The coefficients of static friction (µs) varied for different surface pairs, with rougher surfaces exhibiting higher µs values.

Overall, the experiment provided valuable insights into the behavior of frictional forces and their role in opposing motion. Understanding these coefficients of friction is essential for engineering, design, and various applications in which friction plays a significant role.

## Recommendations:

Based on the results and observations of this experiment, it is recommended to consider surface roughness and orientation when dealing with frictional forces. Engineers and designers should take into account the coefficients of friction for specific surface pairs to optimize the performance of mechanical systems. Further experiments could explore the effects of surface treatments and materials on friction to enhance our understanding of this fundamental force.

Updated: Jan 03, 2024