6. Friction, Experiment and Theory The lab thi wee invetigate the rictional orce and the phyical interpretation o the coeicient o riction. We will mae ue o the concept o the orce o gravity, the normal orce, the rictional orce, tenion, ree-body diagram, and object liding on an inclined plane. The equipment ued will be bloc with a variety o bacing, an adjutable inclined plane and a motion enor with GLX data collecting interace. It i uually ound experimentally that the orce required to lide one object over another i proportional to the normal orce preing the urace together a expreed by F = µ N where µ i called the coeicient o riction and repreent the roughne o the urace in contact. One intuitively eel that the orce hould alo depend upon uch thing a the area o contact and the peed o motion. Let u tudy the quetion experimentally and theoretically. In order to expre the reality that it i harder to mae an object tart moving than to eep the object moving, we can dicu the coeicient o tatic (not moving) riction µ (to get it moving) veru the coeicient o inetic (in motion) riction moving). In general, µ µ. µ (to eep it To tudy the quetion theoretically conider the online imulation at http://mail.mcm.edu/~byov.tihon/demo/phylet/lab5.html It repreent two bloc connected by a tring, where one bloc i located on the table and another bloc i hanging rom the table. The imulation allow changing ma o each o the bloc a well a the coeicient o riction between the bloc and the table. Try variou value or mae and riction coeicient, ee what happen. Notice how acceleration o the ytem change a you change thee variable. Determine the unnown value or mae and coeicient o inetic riction. 41
1. The experimental deign or the irt part o the lab will be very imilar to what you aw in the online demontration. You will be uing a bloc connected by a tring with an additional ma hanging rom the table. You hould alo et up the motion enor in uch a way that it allow you to meaure the peed o the bloc. Thi way you can determine whether or not the bloc i accelerating a it move along the board. Uing thi experimental etup with a horizontal urace, igure out which quantitie you hould plot on the graph in order to determine the coeicient o riction or the bloc liding on the board. Hint 1 and 2 may help to igure thi out. Doe thi graph give µ or µ? Doe µ depend on the value o either F or N? The provided bloc o wood have hoo or pulling and have variou material attached to them to vary the urace in contact. Figure out how to meaure the normal orce and the rictional orce while the bloc i liding acro the board. See Hint 3 and 4 or help iguring out how to do thi. Vary and meaure the correponding calculate the coeicient o riction, µ, rom the graph. N (or ive value) F or a given bloc. Mae a plot and have Excel Repeat or two more bloc. Include all three plot on the ame graph (put a legend on the graph). Which urace ha the highet µ? Doe that mae ene? 2. Set the urace at an angle θ rom the horizontal. Place the object on the urace and increae the angle until it lide. The angle at which the object jut begin to move i deined a the angle o repoe. Figure 1 illutrate thi ituation. From the diagram, it can be hown that there exit a relationhip between the angle o repoe,θ, and the coeicient o riction, µ. Determine thi relationhip and olve or µ in each cae. Doe thi relationhip give µ or µ? (It may help to reread the third paragraph o thi lab and then ee Hint 5.) 42
Uing the ame bloc a beore, compare your reult with thoe determined in Step 1. Figure 1. Finding the angle o repoe. 3. Select a bloc and an angle. Compute the orce required to lide (pull) the object up the inclined plane (See Fig. 2) uing the value o µ determined in Step 1 and 2. Carry out the experiment and compare (via %-dierence) the experimental value with the theoretical value or that type o material. Once again you can ue the motion enor to control whether or not the bloc i accelerating. See Hint 6 or help. Figure 2. Sliding up an incline. 4. I you till have ome time let, determine experimentally the eect o urace area and velocity upon the coeicient o riction o wood-on-wood. Dicu your reult. 43
Hinting Quetion or the Friction Lab Thee quetion hould guide you through the lab i you are having trouble iguring out what to do. Thi i the ixth lab; you will be expected to come up with quetion lie thee on your own next wee. Pay attention to the type o quetion you mut a yourel. 1. Calculating F µ = or each individual value i a reaonable approximation or N µ but thi i one meaurement which ha random error (error which can be reduced by increaing the tatitic, i.e., by repeating the meaurement many time). In the Acceleration due to Gravity -lab, did you get a better reult or the acceleration due to gravity rom the lope o v v. t or rom averaging the individual a value? 2. Compare F = µ N + 0 to y = mx+ b. What hould you plot a the ordinate (vertical axi) and a the abcia (horizontal axi)? What property o the graph give the coeicient o riction, µ? 3. The normal orce i not conceptually equal to the orce o gravity, although in ome cae thee are numerically equal. (Recall that a bathroom cale doe not read your weight, it explicitly read the normal orce you are exerting on the cale.) I you are uing ome bloc, how can you vary (i.e., pic and ue a peciic value o) the normal orce which i exerted on the bloc? 4. I an object i being lowed by a rictional orce, you can indirectly meaure that bacward orce by introducing an additional, meaurable orce which bring the net orce to zero, i.e., which bring the bloc into equilibrium. Remember that equilibrium i a tate in which the acceleration i zero. Can an object move when it i in equilibrium? (What i the dierence between tatic equilibrium and inetic equilibrium?) How can you pull an object acro a board with a peciic, nown orce? 44
5. Are we conidering the bloc during it motion or are we conidering it a it begin to move? 6. Once you now the gravitational orce acting on the bloc, the applied orce i the only variable that i not predetermined (becaue you have already determined µ ). Solve or the applied orce. See Hint 7 i you need more help. 7. I you now the gravitational orce, then you can brea it into it component: along the incline and into the incline. From thi we can ind the normal orce. From that, with µ nown, we can ind the rictional orce. The only unnown r r let i the applied orce. Solve F net = ma or the applied orce. How much weight mut be placed on the hanger? 45