Properties of Friction Lab Report

        The experiment had three main objectives; to experimentally determine the static coefficient of friction using the hanging method; to prove that friction is independent with the areas of contact and evaluate different experimental methods for determining the coefficient of friction. From the experiment, it was established that static friction is proportional to the normal reaction between the surfaces in contact. From task 1, it was established that the hanging mass method can be used to experimentally determine the static coefficient of friction of an object relative to a surface. The results of task 2 indicated that static frictional force is roughly independent of areas of contact. The results of task 3 showed that the inclined plane method can be used to determine the static coefficient of friction and yield similar results to those of the hanging method.

Introduction

            When surfaces come into contact, they exert forces on each other as a result of the electrical attraction and repulsion of the charged particles on the surfaces. The two forces include the normal force and the frictional force. While the normal force functions to keep the surfaces in contact apart from each other, the friction force functions to resist any relative motion between the surfaces (Serway & Jewett, 2008). Frictional force can either be static or kinetic. Static friction acts on two surfaces that are at rest relative to each other. Static friction bonds the surfaces together by resisting any potential motion that may result from the application of any external force. As the external force increase, static friction increases up to a certain limit beyond which the net force on the surfaces ceases to be zero (Wilson & Hernández-Hall, 2014). As such, static friction is a variable force up to a certain maximum value beyond which sliding begins. Once motion begins, kinetic friction ensues and acts opposite to the relative motion of the surfaces in contact. Unlike static friction, kinetic friction is constant under normal conditions. Both static and kinetic frictions depend on the nature of the surfaces and can be determined experimentally. Additionally, both static friction and kinetic friction are proportional to the normal force acting on the surfaces in contact (Serway & Jewett, 2008). Therefore, the ratio of the frictional force to the normal force gives the coefficient of friction (μ) – static coefficient of friction and kinetic coefficient of friction.

Therefore;

The coefficient of static friction is related to the normal force (N) of the object on the surface, when the object just begins to move (Wilson & Hernández-Hall, 2014).

Purpose of Experiment

        The experiment had three main objectives. The first objective was to determine the static coefficient of friction between different materials using the hanging mass method. The second objective was to prove that friction force is independent of the areas of contact. The third objective was to evaluate two different experimental methods for determining the coefficient of friction.

Theory

            According to Newton’s second law of motion, the net force on an object is given by the product of its mass and the acceleration (Serway & Jewett, 2008). Therefore, for an object to be in equilibrium in a particular direction, the net force in that direction must be zero. Precisely, if the net force on an object is zero, its acceleration is zero. For two surfaces at rest relative to each other, the sum of forces must be zero and hence the acceleration is also zero. For an object at rest, the upward force must be equal to the downward force (Wilson & Hernández-Hall, 2014). The downward force is the weight of the object as a result of gravitational acceleration. The upward force is the normal force (N) and must be exactly equal to the downward force if the object is not moving. If an external force is applied in the horizontal direction, then there must be a force acting in the opposite direction that exactly balances the external applied force so that the sum of forces remains zero for the object to remain at rest (Serway & Jewett, 2008). The opposite force is the force of friction that resists the motion of the object on the surface. As earlier noted, the frictional force results from the interaction between the molecules of the object’s surface and those of the surface upon which the object rests. As the applied external force is increased, the frictional force will also increase until motion results. Therefore, when an object is at rest, static frictional force is said to be acting in such a manner as to counterbalance the applied external force (Wilson & Hernández-Hall, 2014).

From equation (i), the static coefficient of friction is given by;

Equation (ii) is the static coefficient of friction for a horizontal plane. For a block resting on an inclined plane as shown in figure 1 below, the static coefficient of friction is given by;

Therefore;

Figure 1: Object on a Slope

An interesting property of friction is its relationship with surface area. Friction force results from forces between two surfaces in contact with each other. It is therefore easy to expect that friction force depends on the surface area in contact. However, frictional force is independent with the magnitude of the area in contact (Serway & Jewett, 2008). The reason is that with a narrower surface – keeping the weight of the object constant – pressure increases thus increasing the frictional force in the same proportion as the surface area decreases. Consequently, the magnitude of frictional force remains the same regardless of the size of the area in contact as long as the weight of the object remains constant.

Methods

Equipment

The following equipments were used in the experiment.

Steel box

Wood box

Plastic box

Wood plank

Pulley

Mass hanger

Mass set,

String 

Table stand 

Right angle clam  

Metal rod

Inclinometer

Procedure

Task 1: Determining Static Friction coefficient using the Hanging Method.

        The surfaces of the box and the friction board were wiped with a moist paper towel to remove any dirt and grit. The pulley was clamped at the end of the friction board as show in the set up below.

Figure 2: Hanging Mass Experimental Set Up

        Mass was then added to determine the hanging mass that was necessary to just start the box moving without a push. Three trials were carried for each mass added on the box, starting with no mass on the box and adding masses of 100g after three trials. The average hanging mass of the three trials to start the system moving from rest was then determined and recorded.

Task 2: Investigating whether Friction Force is Independent of Contact Areas

To accomplish this task, the procedures in task 1 were repeated but this time using larger boxes.

Task 3: Inclined Slope Method

Figure 3: Inclined Slope Method

        To achieve the third objective, the apparatus was arranged as shown in figure 3, with the friction board inclined at an angle θ. The angle was varied to determine the angle necessary to just start the box moving without a push. Three trials were carried for each mass added on the box, starting with no mass on the box and adding masses of 100g after three trials. The length of the hypotenuse and the opposite were recorded. The average of the opposite length for the three trials was then calculated and recorded.

Results and Analysis

Results

Task 1

Table 1 shows the results for task 1

Table 1: Task 1 Results

 Task 2

Table 2: Task 2 Results

 Task 3

Table 3: Task 3 Results

 Analysis

For purposes of analysis, the results for the steel block will be used for the three tasks.

Task 1

Table 4: Analysis of Task 1 Results

From table 4, a graph of F against N was plotted as shown in the figure below.

Figure 4: Graph of F against N

Task 2

Table 5: Analysis of Task 2 Results

 From figure 4, it is clear that there is a linear relationship between the static frictional force (F) and the normal force (N). The two forces are related by the linear equation;

F = 0.1392N + 0.163 ……………. (iv)

Comparing equation (iv) to equation (i), the static coefficient of friction (μ) is thus directly obtained as 0.1392.

Similarly, from figure 5, the two forces are related by the linear equation;

F = 0.1417N + 0.295 …………….. (v)

Also, comparing equation (v) to equation (i), the static coefficient of friction (μ) is thus directly obtained as 0.1417. The values of the static coefficient of friction (μ) from task 1 and 2 are very close to each other. The percentage difference between the two values of μ can be obtained as

             The fact that only a small difference exists between the two values shows that frictional forces are roughly independent of the size of the area in contact. From table 6, the values of tan are in the range of 0.177 to 0.200. From equation (iii) tan θ is the static coefficient of friction (μ). As can be noted, there is a slight difference between the μ obtained in task 1 and that obtained from task 3. The slight difference in the two values results from limitations in the two methods as well as the random errors that exist during experimental measurements. Since only a slight difference exists between the two values of static coefficient of friction (μ), the two methods can comfortably be used to determine the static coefficient of friction of an object relative to a given surface.

Conclusion

        From the experiment, it is clear that there is a linear relationship between the static frictional force and the normal force acting on an object at rest. The results of task 1 show that the hanging mass method can be used to experimentally determine the static coefficient of friction (μ) of an object relative to a surface. On another hand, since there is a slight difference between the values of static coefficient of friction (μ) obtained from task 2 and task 1, it is apparent that static frictional force is roughly independent of areas of contact. Lastly, it is clear from task 3 that the inclined slope method can give fairly the same values of static coefficient of friction (μ) considering that only a slight difference exists between the μ obtained in task 3 and that obtained in task 1

References of  Properties of Friction Lab Report

Serway, R. A., & Jewett, J. W. (2008). Physics for scientists and engineers. Belmont, CA: Thomson-Brooks/Cole.

Wilson, J. D., & Hernández-Hall, C. A. (2014). Physics laboratory experiments. Nelson Education.