Forces And Friction Investigation Lab

Forces and Friction Investigation Lab: Coefficients of Static and Kinetic Friction

Michael Mohamed SPH4U0-C March 20th, 2009

INTRODUCTION: In the study of Newtonian physics is it is useful to consider almost all objects which are not within a vacuum to be subject to the force of friction; in this usage ‘friction’ refers to the overall effect that can be approximated in terms of applied forces by various particles colliding against the object while they are in contact. These forces are typically used in applying resisting forces against objects in motion, as to adhere them to the surfaces that they are lateral to, or in contact with through a motion. An example of this might be air particle friction; when an object moves through a medium comprised of air, the particles of that air colliding against the object, creating a resisting force in the opposite direction of the motion. Because of this, the effect of terminal velocity takes place whereby an object moving with a constant force acting on it (for example, gravity) can only attain a certain speed while in a medium of air due to the forces of air particle friction acting on it in the opposite direction. There are two main types of friction for objects that are relevant to objects that are placed with their surfaces in contact, excluding the air particle friction force. One is static friction; this can be described as the friction which keeps a body that is not moving resistant to forces that could potentially put it in motion. The force needed to overcome static friction is specific for two objects of specific material types, as well as the mass of the object with a force being applied to it; when static friction is overcome the object will enter motion of some kind. While the object is in motion, there is still friction acting on it which resists it from moving with acceleration; while this force is not overcome the object will remain at a constant speed. This is known as kinetic friction; when it is overcome the object will begin moving in non-uniform motion, with the force affecting the acceleration being the difference between the applied force and the force of kinetic friction. In both cases, the force of friction can be related by a coefficient which is specific to the two materials in contact; this force is equal to the applied force needed to overcome each type of friction divided by the normal force acting on the object, and it is represented by the symbol μ. For example, the coefficient of kinetic friction can be described as the force needed to be overcome in order to cause an object to move non-uniformly divided by the normal force acting on the object, or μK = FK/FN. Similarly, the coefficient of static friction can be described as the force needed to overcome inertia on a

non-moving object divided by the normal force acting on the object, or μS = FS/FN. These coefficients are useful in calculating the total force on an object against a surface where the materials of the surface and the object are known.

PURPOSE: The purpose of this lab was to investigate various ways of calculating coefficients of static and kinetic friction through experiments both using and not using Newton scales. The question of how one can measure static friction in two ways is addressed and the results of the experiments compared. For static friction, a comparison was made between the calculated coefficient using a Newton scale and the coefficient calculated without a Newton scale; percent difference was calculated to try and show possible sources of error from one compared to the other. A comparison was also made from the calculated coefficients of static friction, as the coefficient of kinetic friction is typically of a lower value.

METHOD: Experiment 1 - Static Friction without Newton scale: 1. A measured plywood surface was attached to a retort stand by a retort clamp at a very low height above the surface of the table it was placed on. 2. The plywood was attached such that it would form a right angle triangle with the retort stand perpendicular to the table, with an acute angle formed between the plywood and the table. 3. A massed textbook was placed onto the very top edge of the plywood surface. Because of the low height of the retort clamp to the table, the textbook was stable and did not move. 4. A ruler was held against the retort stand, and the clamp itself was loosened to allow for adjustment. 5. The retort clamp was raised higher and higher in very small increments, causing the angle formed between the end of the plywood and the table to increase. 6. When the retort clamp reached a height at which the textbook began to fall down the slope formed by the plywood surface, the retort clamp was tightened and the ruler held against the retort stand was used to measure the height of the top of the plywood to the table. 7. Steps 5 and 6 were repeated 4 times more to ensure accuracy of measurements. Experiment 2 - Static Friction with a Newton Scale 1. A measured piece of plywood was attached to a retort stand by a retort clamp at a low height from the table that it was resting on. 2. A massed textbook was tied to a piece of string going through the middle of the book, and then placed on top of the plywood surface. 3. The height from the top of the plywood surface relative to the table it was resting on was measured. 4. Using a Newton scale attached to the string going through the textbook, an applied force was measured pulling in the direction upwards the slope of the plywood surface; the force was not high enough to move the textbook. 5. The force applied was slowly increased while the measurement of the force was monitored closely. At the point when the textbook began to

move, the force applied decreased. The force that was measured before the textbook began to move was measured. 6. Steps 4 and 5 were repeated 4 times more to ensure accuracy of measurements. Experiment 3 - Kinetic Friction with a Newton scale: 1. A measured plywood surface was attached to a retort stand by a retort clamp held at a low height from the surface of the table it was resting on. 2. The height of the plywood surface from the table was measured. 3. A massed textbook was attached to a tied string going through the middle of the book. 4. The textbook was place on the inclined plywood and a Newton scale was attached to the string going through the textbook. 5. An applied force was used to drag the textbook up the inclined surface using the Newton scale, the force applied was measured. 6. Step 5 was repeated four times to ensure accuracy.

MATERIALS: retort clamp textbook sheet of plywood mass scale calculator

retort stand string Newton scale ruler pencil

OBSERVATIONS: Table 1 - Static Friction without Newton Scale Measurement Value

Length of plywood Mass of textbook 1st height measure 2nd height measured 3rd height measured 4th height measured 5th height measured Average height measured

84.2 cm 2.005 kg 24.6 cm 25.4 cm 24.9 cm 24.8 cm 24.8 cm 24.9 cm

Table 2 - Static Friction with Newton Scale Measurement Length of plywood Mass of textbook Height above table 1st Newton scale reading 2nd Newton scale reading 3rd Newton scale reading 4th Newton scale reading 5th Newton scale reading Average Newton scale reading

Value 84.2 cm 2.005 kg 19.3 cm 11.4 N 11.5 N 11.7 N 11.9 N 11.5 N 11.6 N

Table 3 - Kinetic Friction with Newton Scale Measurement Length of plywood Mass of textbook Height above table 1st Newton scale reading 2nd Newton scale reading 3rd Newton scale reading 4th Newton scale reading 5th Newton scale reading Average Newton scale reading

Value 84.2 cm 2.005 kg 19.3 cm 9.3 N 9.5 N 9.8 N 10.0 N 8.9 N 9.5 N

RESULTS: Results 1 - Static Friction without Newton scale: In this case, one value that can be found is the amount of force acting on the textbook in the positive direction of the x-axis, this should be equal to the frictional force acting upon the textbook in the negative direction of the x axis at that time. When the specific angle was reached at which the textbook began to move, the force was enough to just overcome the force of static friction. Using the height above the ground and the length of the plywood, Pythagorean Theorem can provide the angle of the plywood’s incline; this angle is all that is needed to find the coefficient of friction.

Normal Force: Force of Static Friction: Force of Gravity: Acceleration due to Gravity: Mass of textbook: Coefficient of Static Friction: FG) = tan(θ) Angle of Incline:

FN = -FGy = -(cos(θ) * FG) FS = -FGx = -(sin(θ) * FG) FG = g * m g = 9.8 m/s2 [down] m = 2.005 kg μS = FS/FS = (sin(θ) * FG) / (cos(θ) * θ = sin-1(24.9 cm/84.2 cm) = 17o

Therefore μS = tan(17) = 0.306 Results 2 – Static Friction with a Newton Scale: In this case the force being applied to the object by the Newton scale should be equal to the force acting on the object in the positive direction, the force of gravity in the x-axis and the force of static friction. Force Applied: FA = -(FGx+FS) Force of Gravity: FG = 9.8 m/s2 * 2.005 kg = 19.649 N Angle of Incline: θ = sin-1(19.3/84.2) = 13.251o Force of Gravity in x-axis: FGx = sin(θ) * FG = -4.304 N Force of Static Friction: FS = -(FGx+FA) = -(-4.304 N + 11.6N) = -7.296 N Normal Force: FN = -FGy = cos(θ) * FG = -19.126 N Coefficient of Static Friction: μS = FS/FN =7.296/19.126 = 0.371 As can be seen, there is some difference in the values for μS found. Results 3 – Kinetic Friction with Newton Scale: In this experiment, while the object moves at a constant speed up the incline, the force applied should be equal to the sum of the force of gravity in the x-axis and the force of kinetic friction. Using the angle of incline, this along with the normal force can be found; the two can then be divided to provide the coefficient of kinetic friction. Angle of Incline: θ = 13.251o Normal Force: FN = -19.126 N Force of Gravity in x-axis: FGx = -4.304 N Force of Kinetic Friction: FK = -(FGx + FA) = -(-4.304 + 9.5) = -5.196 N

Coefficient of Kinetic Friction: μK = FK/FN = 5.196/19.126 = 0.272

Therefore μK < μS

DISCUSSION: Interpretation of Results The results from this experiment follow the trend seen in the vast majority of objects with a friction force between them; the coefficient of static friction is higher than the coefficient of kinetic friction. The results are realistic in terms of being a coefficient of friction between wood and paper. However, the 2nd experiment had a much higher coefficient of static friction found as compared to that of the 1st experiment; this shows that between one of the two experiments there was a source of error. Possible Sources of Error The most common source of error would be the fact that a person was the one applying the force measured on the Newton scales as well as a person reading the scale as motion was taking place; the fact that the coefficient of static friction is overcome at a very exact measure of force made it difficult to accurately read on a Newton scale while the change in

force between static and kinetic friction was instantaneous. Another source of error would be the equipment used: the textbook was used to measure friction against the plywood was used and uneven on either side of the cover with many areas of dirt, indents, or torn paper. The Newton scales used themselves were very well used and had a slightly unstable calibrating mechanism. The string used to tie the scale to the textbook may not have been perfectly even, dividing out the force to one side of the textbook more than the other, uneven as compared to the straight two dimensional diagrams used to calculate the coefficients. Percent Difference between Experiments 1 and 2 μS % Diff = 2|x1-x2|/(x1+x2) * 100 = 2|0.371-0.306|/(0.371+0.306) * 100 = 19.2% This percent difference is taken due to the difference between the values of μS calculated. This shows that the percent difference is fairly high; due to the aforementioned difficulties with measuring coefficients of static friction using a Newton scale, the results of the first experiment (μS = 0.306) should be considered the more accurate result of the two.

CONCLUSION: In terms of investigating coefficients of friction, a few things can be noted. The first is that while using a Newton scale may provide a measured amount of force being applied to the object, the recoil caused by the switch from static to kinetic friction (due to the object being forced out of stability) tends to make measuring the force applied difficult. In comparison, a method of measuring static friction while only measuring the angle of the inclined surface that it is on as the gravitational force pulls it down provides a simple means of calculating the coefficient without much measurement or calculation (μS = tanθ). When these results were compared to those of the coefficient of kinetic friction, the measurement using a Newton scale is roughly accurate; reading the Newton scale is not difficult as the force applied remains constant at a magnitude that is equal to the force of kinetic friction, causing uniform motion. The coefficient of kinetic friction can be said

to be calculated with rough accuracy, and as expected it is lower than the coefficient of static friction calculated. Overall, the conclusion can be made that using a Newton scale works well for measuring kinetic friction, and poorly for measuring static friction.