Friction Experiment. 1. Introduction. 2. Background Force. Science and Mechatronics Aided Research for Teachers

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1 Science and Mechatronic Aided Reearch for Teacher Introduction Friction Experiment by Sang-Hoon Lee, Saul Harari, Hong Wong, and Viram Kapila Puhing a heavy box that i lying on the ground can be quite difficult for even a large mucular adult. However, if the ame box i placed on a wheeled dolly intead, a mall child may have little difficulty moving the box. How i thi poible? Doe the dolly omehow mae the box any lighter? Friction i at the root of thi iue. If you try to move the box while it i on the ground, you will encounter a ignificant amount of friction, which mut be overcome. Placing the box on the dolly reduce the friction preent in the ytem and mae it much eaier to move the box. It may ound a though friction i omething that mae life overly difficult and that you would be better off without it. The truth i very much the oppoite, however. Car ue friction both to enable them to move and to brae while in motion. Have you ever tried to wal on ice? Even on ice there i a mall amount of friction. Without friction, waling would be impoible. In thi experiment we will claify the variou form of friction that are encountered in everyday life. 2. Bacground 2.1. Force What i commonly referred to a friction i actually a frictional force. Therefore, to properly define friction, we mut firt introduce the concept of force and velocity. Force and velocity are vector quantitie; they have both a magnitude and direction. Velocity can be thought of a the peed in a pecified direction, with which a given object i traveling. Force i the mechanim through which the object accelerate, or undergoe a change in it velocity. A body that i at ret i one in which the reultant force, the um of all force acting on the body, i zero. Such an object i aid to be in equilibrium. Although many different form of force exit, there are two broad claification that are commonly ued to categorize force. Firt, we ditinguih between conervative and diipative force. Conervative force act upon an object in a manner uch that the total energy of the object i conerved. Diipative force are one that reduce the total energy of the object upon which they act. Friction i a diipative force. A different way to categorize force i to ditinguih between contact and field force. Contact force, a the name implie, rely upon phyical contact to act on a body. Field force require no phyical contact to act on a body. Friction i a contact force. Gravitational and magnetic force are common example of field force. See [8] for more detail. We will now define and dicu a few type of force that are of direct importance to our dicuion on friction. Gravitational force Gravity i an attractive force that exit between two mae. The magnitude of the force depend on the proximity of the mae involved, a well a the magnitude of the mae. At large ditance, and/or if the mae of interet are of mall quantity, the effect of gravity can be ignored. That i why atronaut in outer pace float freely, and atronaut on the moon bounce along a they do. We approximate the gravitational force that act on an object on Earth a F g = mg Diviion of Engineering Education & Center

2 Science and Mechatronic Aided Reearch for Teacher where m i the ma of the object and g i the free-fall acceleration. Thi value i only an approximation becaue the magnitude of g depend on the altitude of the object a well a the latitude of the location. However, becaue the patial difference in acceleration due to gravity are o mall, the approximation i well jutified. The magnitude of the gravitational force exerted on an object i referred to a it weight. See [8] for more detail. ormal force The normal force i a contact force that act in the normal direction, i.e., perpendicular to, the contact urface between two object. For an object ubjected to no force other than gravity, the magnitude of the normal force i equal to the component of the gravitational force that act normal to the urface, but it act in the oppoite direction. See [2, 8] for more detail. Figure 1 depict a free-body diagram of a ma, m, lying on a horizontal urface, where the normal force,, i equal in magnitude to the gravitational force mg. m 2.2. Friction Figure 1: Free-body diagram of a ma lying on a horizontal urface There are different form of frictional force that occur. When friction act on an object that i at ret, we refer to the frictional force a tatic friction. An object that i in motion i ubject to inetic, or dynamic, friction. Friction i a reitive force, one that damp out motion in dynamic ytem and prevent movement in tatic ytem. Friction occur becaue an object interact with either the urface it lay upon, the medium it i contained in, or both. Only in a complete vacuum can a ytem be free of friction. Static friction When you want to puh a heavy object, tatic friction i the force that you mut overcome in order to get it moving. The magnitude of the tatic frictional force, f, atifie f µ where µ i the coefficient of tatic friction, a dimenionle contant that depend on the object and the urface it i laying upon. From thi equation it i clear that the maximum force of tatic friction, f,max, that can be exerted on an object by a urface i mg Diviion of Engineering Education & Center

3 Science and Mechatronic Aided Reearch for Teacher f, max = µ Once the applied force exceed thi threhold the object will begin to move. A common example of a tatic friction force i that of a tationary ma on an incline. Figure 2 depict the free-body diagram of thi cae.. y x f θ mg Figure 2: Free-body diagram of a ma on an incline If the angle at which the ma begin to lide i nown, we can determine µ by decompoing the force into the Carteian coordinate, x, y, a given in Figure 2. Since we are intereted in the intant at which movement begin, we are dealing with an object in equilibrium. Thu, the reultant force in both the x and y direction mut be zero. Analyi of the force in the x direction yield Following a imilar procedure for the y direction yield However, we now that at the intant that the ma begin to move f f = mg inθ. (1) = mg coθ. (2) = f =. (3), max µ Thu, by ubtituting (2) into (3) and equating the reult with (1) we can olve for µ a follow f = µ mg coθ = mg inθ µ = tanθ. Kinetic friction Once the force applied on a ma exceed f, max and the ma begin to move, a inetic friction force, f, exit. Kinetic friction coefficient are generally le than tatic friction coefficient, which i the reaon that it i much eaier to eep a heavy object in motion than it i to tart it in motion [4]. The magnitude of the inetic frictional force i given a follow f = µ Diviion of Engineering Education & Center

4 Science and Mechatronic Aided Reearch for Teacher where µ i the coefficient of inetic friction and i approximately contant. Figure 3 i a plot of frictional force veru applied force [1, 8]. The light fluctuation in the inetic region of the plot are due to the light dependency of µ on the peed of the object [8]. Figure 3: Plot of frictional force veru applied force Table 1 lit the coefficient of tatic and inetic friction for variou object/urface combination [5, 8]. The coefficient of tatic friction i le than that of inetic friction for all cae in the table except Teflon on Teflon. Material Table 1: Coefficient of tatic and inetic friction Coefficient of Static Friction µ ) ( Coefficient of Kinetic Friction µ ) Steel on Steel Aluminum on Steel Copper on Steel Rubber on Concrete Wood on Wood Gla on Gla Waxed wood on Wet now Waxed wood on Dry now Metal on Metal (lubricated) Ice on Ice Teflon on Teflon Synovial joint in human Rolling friction Rolling friction i a pecial cae of inetic friction. When we ay that a wheel roll without lipping, we are implying that the wheel i ubjected to rolling friction. The motion of a wheel under rolling condition i not affected by inetic friction. There are no diipative force acting on the wheel ubject to rolling friction, under ideal condition, becaue the wheel doe not lip at the point of contact. A a reult, rolling friction doe not impede on the motion of the wheel. However, once rolling ceae, inetic friction i the only frictional force acting on the wheel. ( Diviion of Engineering Education & Center

5 Science and Mechatronic Aided Reearch for Teacher In non-ideal condition, rolling friction on a wheel doe act a an energy diipative force due to trace lippage caued by flexing of the wheel. Experimentally, the coefficient of rolling friction between the tire and the road i found to be , wherea the coefficient of tatic friction between the tire and the road i found to be 0.8. See [2] for more detail. 3. Equipment lit Board of Education (BOE) with Baic Stamp 2 (BS2) The combination of the BS2 embedded within the BOE will erve a the microcontroller that monitor the experiment that you are about to do. The BS2 i a 24 pin Dual Inline Pacage (DIP) integrated circuit (IC). It i baed on Microchip Inc. PIC 16C57 microcontroller. The BS2 i powered by a 6-14V direct current (VDC) power upply. An onboard voltage regulator provide a teady 5VDC output to the BS2. The BS2 come with ROM, 2KB Electronically Eraable Programmable ROM (EEPROM), and a mall amount of RAM. The BS2 i programmed in PBaic language, the intruction et that i tored in the BS2 ROM. The uer defined program i downloaded into the EEPROM from a PC to the BOE uing a DB-9 erial cable. The exce EEPROM can be ued for long term data torage. The BS2 ha 16 general purpoe digital input/output (I/O) pin that are uer defined. The high poition on a digital I/O pin refer to a 5VDC and a low poition on a digital I/O pin refer to a 0VDC (ground potential). Each pin can ource (upply) a maximum current of 20mA and in (draw) a maximum current of 25mA. The 16 I/O pin on the BS2 at any given time can ource/in a maximum of 40mA/50mA. If uing an external 5VDC voltage regulator, thee limit apply to each group of 8 pin, P0-P7 and P8-P15. Exceeding thee current ource/in limit or etablihing a voltage on a pin greater than 5VDC will damage the BS2. See [6, 7] for more detail. A limitation that often arie when uing the BS2 i the lac of upport for floating point variable. Utilizing floating point operation lie diviion in the abence of floating point variable may lead to mathematical error due to truncation. The larget variable or contant that can be tored on the BS2 i of word ize (16 bit), which ha a numerical range of 0-65,535 in decimal notation. A BOE and BS2 are depicted in Figure 4 [3]. The BS2 i placed, in the ame orientation a hown, in the IC ocet in the lower left corner of the BOE. Figure 4: Parallax Board of Education with a Baic Stamp 2 at right Static friction experiment tet bed The tatic friction coefficient tet bed will be ued to experimentally determine the coefficient of tatic friction between variou urface. It conit of a horizontal bae and a plate that can be rotated from a level plane that correpond to θ = 0, and where the vertical poition correpond to θ = 90. The tet bed relie upon µ = tanθ, an equation that we have previouly derived. The plate, which i Diviion of Engineering Education & Center

6 Science and Mechatronic Aided Reearch for Teacher connected to the bae through a hinge, i rotated by a DC motor. The DC motor i driven by a regulated 12 VDC external power upply. An H-Bridge i ued to control the rotational direction of the DC motor. An InfraRed (IR) tranmitter and receiver pair i ued to detect movement of the ma. The pair ha been mounted on the oppoing idewall of the plate facing each other. The IR tranmitter continuouly end an infrared pule toward the receiver. When the ma tart to lide, it interrupt the infrared beam. To enure accuracy, the experiment mut be conducted o that the firt intant of the ma movement i detected. To achieve thi accuracy, a topper ha been placed at the free end of the plate uch that by placing the ma nug againt it the IR beam will be tripped the intant the ma begin to lide. Once the IR receiver ha been tripped, the BS2 hut the motor down. The angle at which the ma begin to lide i meaured by a rotary potentiometer connected to the hinge on which the plate turn. A contant 5VDC voltage i applied acro the full reitance of the potentiometer. The wiper rotate along with the plate, and the voltage between the wiper and one end of the potentiometer i meaured. Since the BS2 i a digital device and the quantity being meaured i an analog voltage, an Analog to Digital Converter (ADC) IC i utilized. The quantization number, Q, of an ADC depend on the number of bit the ADC ha and on the pan (range of value) that i being digitized. Q for an n -bit ADC i given by Q = V pan n where V pan i the voltage pan to be digitized. Thi tet bed ue an ADC0831 from ational Semiconductor, an 8-bit, ucceive approximation converter that i eaily interfaced with the BS2 uing the PBaic hiftin command. See [6, 7] for more detail. A an 8-bit device it can convert an analog ignal into 256 dicrete level. To maximize the enitivity of the ADC the offet and pan voltage were provided to the ADC by adjuting two potentiometer to provide the proper voltage. A topper ha been intalled at the foot of the plate to prevent the ma from falling down. Circuit chematic for the tatic friction coefficient can be found in Appendix A. Figure 5 i an overhead view of the tet bed. The DC motor can be een in the lower left hand corner of the figure. The potentiometer can be een in the upper left hand corner. The topper that prevent the ma from falling of the plate can be een on the left hand ide of the figure. The electrical circuitry ued by the tet bed can be een on the right hand ide of the figure. 2 Potentiometer Stopper ADC with pan and offet Circuitry DC motor H-Bridge Figure 5: Overhead view of the tatic friction coefficient tet bed Diviion of Engineering Education & Center

7 Science and Mechatronic Aided Reearch for Teacher Figure 6 i a cloe up view of the tet bed. In the upper left hand corner of the figure the IR receiver i viible. In the lower right hand corner of the figure the IR tranmitter i viible. The topper ued to mar the tarting poition of the ma can be een behind the ma. IR receiver Stopper IR tranmitter 4. Experimental procedure 4.1. Static friction experiment Figure 6: A view of the tatic friction coefficient experiment Figure 7 i an illutrative diagram depicting the functionality of thi experiment. A ma i placed on the plate, which i then rotated until the ma begin to lide down the inclination. An IR receiver detect the firt intant of the ma motion. IR tranmitter IR receiver θ Figure 7: Static friction coefficient experiment Goal: 1. Experimentally verify that the coefficient of tatic friction for variou urface. Static friction experiment procedure 1. Connect the BS2 to the tet bed with the DB-9 adapter located on the tet bed, and to a computer with another DB-9 erial cable. 2. Connect the BS2 to a 9VDC power ource, either a power adapter or battery can be ued. 3. Download the StaticFriction.b2 file to the BS2. 4. At the prompt place the ma on the tet bed, lining it up properly. 5. The BS2 will then rotate the plate through an arc (0 to 90 ) until the IR detector i tripped. 6. The BS2 will calculate µ from the angle at which the IR detector wa tripped. 7. To continue with thi experiment follow the prompt regarding retarting the experiment. Diviion of Engineering Education & Center

8 Science and Mechatronic Aided Reearch for Teacher Dicuion Which material ha the highet coefficient of tatic friction? Doe thi agree with your intuition? What do you thin determine the coefficient of tatic friction? Surface area? Contact area? See [2, 4, 8] for more detail. Once the ma begin to lide doe it move moothly, or doe it undergo top and go motion? What poible explanation for the motion can you thin of? 5. Suggeted Project 1) Kinetic and tatic friction coefficient detector: Devie a mean of meauring the coefficient of inetic friction. It may be poible to modify the tatic coefficient experiment to accomplih thi project. 6. Reference [1] Online: web ite of the Phyic Department at Concordia Univerity containing phyic lecture. [2] Online: educational web ite for phyic, math, chemitry, mechanic, and other natural cience, by Carl R. ave. [3] Online: web ite of Parallax, Inc. manufacturer and ditributor of Baic Stamp microcontroller containing technical pecification and uer manual. [4] Online: web ite of PhyicEq.com containing high chool level phyic tutorial, by Stephen Embree. [5] Online: web ite of Phylin.com containing coefficient of tatic and inetic friction. [6] Online: web ite of Stamp in Cla containing educational reource for Baic Stamp microcontroller. [7] V. Kapila, Coure ote for Mechatronic ME 3484, Polytechnic Univerity, Broolyn, Y, (2003). [8] R.A. Serway and R.J. Beichner, Phyic for Scientit and Engineer. Saunder College Publihing, Orlando, FL, 5 th Ed., (2000). Diviion of Engineering Education & Center

9 Science and Mechatronic Aided Reearch for Teacher Appendix A: Circuit chematic Figure A1: Circuit chematic of the ADC ued to digitize the angle of inclination Figure A2: Circuit chematic of the IR tranmitter/receiver pair ued to detect motion Diviion of Engineering Education & Center

10 Science and Mechatronic Aided Reearch for Teacher Figure A3: Circuit chematic of an H-Bridge uing BJT tranitor Diviion of Engineering Education & Center