Determining the Factors that Affect Friction Using a Force Sensor

Transcription

1 Determining the Factors that Affect Friction Using a Force Sensor Yadesh Prashad, Mai Wageh, Saad Saleem, Timothy Yang, ThAnoja Gnanatheevam December 29 th, 2011 Abstract A force sensor is attached to an elastic band that pulls a wooden container at constant velocity. The purpose of this lab is to establish what factors affect friction by testing different variables. In the first lab, we altered the surface area that the box occupies by measuring the force of tension through the sensor. The results were then graphed through a computer program, and from it, the maximum force of static friction and the average force of kinetic friction were obtained. In the second lab, the surface in contact with the container is changed and the frictional forces are gathered through the graphs. In the last lab, the variable altered is the mass as more is added through each test and the graphs are interpreted. With the data collected from the frictional forces, graphs are made to compare the varying results within each lab. Our results concluded that surface area is an independent variable where as surface type and mass contribute to the magnitude of the force of kinetic and static friction. 1 INTRODUCTION This experiment was conducted to determine how certain factors would affect the magnitude of friction acting on an object. The factors included: the mass of the object, the size of the contact area, the smoothness of the object and contact surface and the types of materials. Our experiment was designed so that the tensional force could be measured as a mass was pulled along a surface at a constant velocity. Figure 1 illustrates how the experiment was generally conducted. For each factor we tested, the experiment was changed slightly. When we tested mass, we added additional mass to the experiment. Before doing so, we predicted that as the mass increased so would the frictional force. The reasoning for this is that a heavier object requires more energy to pull than a lighter object along the same surface. When we tested how contact area affects friction we turned the mass on its side so that its contact with the wooden surface was decreased from cm 2 to cm 2. We predicted that in this experiment, the frictional force would be decreased with less contact as there would be less bonding between the surfaces and therefore less friction. When we tested how the smoothness of the surface affected friction, we tested this by changing the surface type. We predicted that the smoother surface would have more friction as more bonds would be

2 formed between the two surfaces. For the last portion of the experiment, we tested types of materials in contact with each other. We were unsure exactly what would happen with the frictional force between different materials. During the experiment we used a mass, an elastic band, a wooden plank and a force sensor. Being pulled at constant velocity Mass Elastic Force Sensor Figure 1: Illustrative design of the apparatus used. Wooden Plank Lab bench 2 Theory F N F k M F T F g Figure 2: A free body diagram of the forces acting upon the rectangular container.

3 For the first experiment we measured the tension force (F T ) in the elastic band using a force sensor, we measured the mass of the box on a scale balance and we measured the surface area with a ruler. Since we kept velocity constant in every trial the net force (F net ) was equal to zero. So we used Newton s first law to find the magnitude of static friction (f s ) and kinetic friction (f k ) When the box was not moving: When the box was moving: F T changed when the box started moving. f! = F!! (1) f! = F!! (2) In the second experiment we used the same method to find F T, m, f s and f k then we used Newton s first law to find the normal force (F N ) Acceleration due to gravity (g) F! = F! (3) F! = mg (4) F! = mg (5) After we found F N we used it to find the coefficients of static friction (µ s ) and kinetic friction (µ k ) Coefficient of static friction: μ! =!!!! (6) μ! =!!!" (7) Coefficient of kinetic friction: μ! =!!!! (8) μ! =!!!" (9)

4 3 Experiment This experiment involved the use of a force sensor to measure the force of tension on the string. This string was attached to the force sensor on one side and a block of wood on the other side (Figure 1). For the one portion of this experiment, we determined how the mass of an object affected the kinetic force of friction acting on the object, and how mass affected the maximum static force of friction. We did this by connecting the string to the force sensor and a wooden box, as well as a mass set of which we used different components of to be placed inside the wooden box as to change the mass of the object itself, and using the program connected to the force sensor we found tension, and from the tension we found out the kinetic force of friction and the maximum static force of friction, and using the equation (µ K = F K /F N or µ s = F smax /F N ) and the normal force (F N ) we found out by multiplying g (9.8 m/s 2 ) by the mass of the box (1.63kg), we determined what the coefficient of kinetic friction (µ K ) was, and what the coefficient of static friction (µ s ) was. By utilizing the data from the graph, we analyzed the change in masses in each trial compared to the change in friction. Through this information, we determined how the mass of an object affected the kinetic and static forces of friction when everything except the mass was constant. For another portion of this experiment, we determined how different surface types affected friction. To do this, we used the same wooden block, the same string, and the same force sensor. The variation to this portion was that the mass be kept constant and only the surface type changed. The two types of surfaces we tested our theory on were a wooden plank and a lab desk. We used the same procedure as well; measuring the force of tension using the force sensor, determining the force of friction and the coefficient of friction based on the results we obtained from the force sensor program, then analyzing the graphs to determine how the two different surface types affected friction. We determined how the different surface types affected the kinetic and static forces of friction when everything except the surface type was kept constant. For a third portion of this experiment, we determined how contact surface affects friction. We used the same procedure as the previous portion of this experiment, but we changed the surface area in this part. In the first trial, the surface area was cm 2 of the box making contact with the wooden plank surface, and the second trial was cm 2 of the box in contact with the wooden plank. Again, we determined the force of tension using the program connected to the force sensor, and with this we found the magnitude of the kinetic and static forces of friction. We then analyzed the results and found out how the force of friction changed depending on each of the different surface areas.

5 4 Data Weight of Box (N) Contact Surface Area vs. Friction Weight of Masses (N) Fn Fsmax Fk 1.26 (m2) (m2) Table 1: This table compares how surface area affects the amount of friction an object receives from a force. In this case, the force acting on the object is tension from a string which is pulled at a constant velocity. Two surface area of a box were used to conduct this experiment. Based on the information gathered from these two experiments, we can conclude that the greater the surface area, the less kinetic and static friction it has. Graph (1) 2.5 Contact Surface Area vs. FricAon F r i c 2 t i o n al F o rc e Fsmax Fk (N) Contact Area (m2) Figure 3: The graph shows that as the contact surface area is decreased, the frictional force increases.

6 Weight of Box (N) Surface Type vs. Friction Weight of Masses (N) Fn Fsmax Fk Wood Lab Desk Table 2: This table compares how surface type affects the amount of friction an object receives from a force. The two surface types that were used included wood, and a lab desk. A box with a weight of 1.63 N was pulled by a string with constant velocity on both surface types. From the results, it was revealed that the lab desk applied more friction to the object because the value of Fsmax and Fk was significantly higher than the friction applied by the wood. Based on the information gathered from these two experiments, we can conclude that friction does depend on the smoothness and roughness of a surface type. In the experiment the lab desk was significantly smoother than the wood. Graph (2) Surface Type vs. FricAon F r i c t i o n al F o rc e ( N ) Fsmax Fk 0 Wood Surface Type Lab Desk Figure 4: The graph verifies that the smoother surface requires significantly more force to pull an object across than a rougher one.

7 Total Weight vs. Friction Weight of Box Weight (N) of Fn (N) Fsmax (N) Fk (N) (N) Masses (m) x x x x Table 3: This table compares how the total weight of an object affects the amount of friction an object receives from a force. Four experiments were conducted using four different masses of 0.50 kg, 0.75 kg, 1.0 kg, and 1.25 kg. These masses were placed in a box and pulled by a string at a constant velocity. Based on the information gathered from these experiments, we can conclude that the greater the weight, the more friction an object will experience. Graph (3) 6 Total Weight vs. FricAon FricAon Force (Newtons) Fsmax 5.15 Fk Weight (Newtons) Figure 5: This graph verifies that as the weight of an object increases, so does the force required to move that object.

8 Errors: While conducting these experiments, there were many systematic and human errors that occurred. A key error that may have jeopardized our data would have been the pulling of the box at a constant velocity. It is very likely that the force applied to the string was different for every experiment and not pulled at a constant velocity. Another factor would be the surface type of the wood that the object was pulled against. The wood had a staggered surface due to the mix of many different types of wood. This would result in a inconsistent amount of friction due to the collection of different wood surfaces. 5 Conclusion This report has discussed three of the many different factors that affect friction. The objectives of this lab were to develop an understanding of how friction was affected by three different factors: the mass of the object, the types and smoothness of the surface, and the size of the contact area. We hypothesized that the more surface area the object covered, the more friction there would be, as well as the smoother the surface, the more friction would be present, and finally, the more mass there was, the more friction there would be. Two out of these three objectives were met. The experiment which involved surface area did not give us the results we predicted. We found that the frictional resistance force between two surfaces is actually independent of the area of contact, meaning that the contact surface area will not affect the magnitude of friction. This lab has extended our knowledge even further to the important topics of how different factors affected friction. In the lab, the force sensor allowed us to determine the magnitude of tension acting upon the string. Besides tension measurement, the force sensor helped us find the force of static and kinetic friction and the coefficients of static and kinetic friction. Using this, we analyzed the data from our experiments, and came to the conclusion that the contact surface area is an independent variable, whereas surface type and smoothness, and the mass of an object indubitably contribute in affecting the magnitude of the force of friction. 6 Acknowledgements We would like to extend our gratitude to Mr. Murzaku and Mississauga Secondary School for providing us with the materials necessary to execute this experiment.