# Experiment 6: Friction

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1 Experiment 6: Friction In previous lbs we studied Newton s lws in n idel setting, tht is, one where friction nd ir resistnce were ignored. However, from our everydy experience with motion, we know tht friction must be tken into ccount for relistic description of prcticl situtions - it is something we cnnot ignore. Frictionl forces ct between two surfces nd oppose their reltive motion. They occur becuse of surfce irregulrities, such s defects, nd moleculr forces (or bonds) between the mterils. In this lb we will study frictionl forces between vrious objects on different types of surfces. There re two types of friction: kinetic nd sttic. Kinetic friction is the friction between surfces in reltive motion. When sliding n object cross nother surfce, microscopic bumps nd defects tend to impede nd resist the motion (even the smoothest surfces re rough on the microscopic scle). This is the type of force tht brings rolling bll to rest or costing cr to stop. Experimentlly, it is observed tht the force of kinetic friction is proportionl to the norml force cting between the surfces: if you increse the norml force, the surfces re crushed more together, incresing the contct re, nd thus incresing the frictionl force. Mthemticlly we cn write the force of kinetic friction s F k = µ k F N (1) where F N is the norml force between the two surfces in contct with one nother nd µ k is the coefficient of kinetic friction. The coefficient of kinetic friction is dimensionless quntity (no units) tht depends on the properties of the two surfces. µ k rnges from 0.01 for very smooth surfces to 1.5 for very rough surfces. So, for exmple, if we wnt to push n object with constnt speed on very smooth horizontl surfce (such s ice), we must pply round 1% of its weight, wheres if we wnted to push the object on rough surfce (dry concrete) we might need to push the object with greter force thn its own weight. Sttic friction describes the frictionl forces between the surfces of two objects tht re t rest with respect to ech other. The sttic friction between the two surfces is described by the coefficient of sttic friction µ s. Experimentlly, is it found tht the mximum vlue for the sttic frictionl force is proportionl to the norml force between the two surfces. Thus the sttic frictionl force F s is F s µ s F N (2) Since the objects re t rest with one nother, more moleculr bonds re ble to form mking the object hrder to move nd so greter force is needed to strt motion when compred to the kinetic friction cse. Therefore µ s is generlly greter thn µ k. Grphiclly, this is shown in Figure 1: As you increse the force, the sttic friction force increses linerly until the pplied force F equls µ s F N. After this point the object breks wy nd the friction force flls to the kinetic friction vlue. 1

2 fr fr = μsfn sttic kinetic 0 no motion sliding F Figure 1: Force of friction (fr) s function of n externl force F pplied to n object tht is initilly t rest. Experimentl Objectives The purpose of this lb is to construct reltionship between frictionl forces nd the norml force on n object, to clculte the kinetic nd sttic coefficients of friction for vrious objects nd surfces nd to ultimtely gin solid understnding of sttic vs kinetic friction. In this lb you re given pulley sensor tht cn mesure ccelertion, force sensor, string, friction crts with different surfces (cork, felt, nd plstic), nd different surfces (sheet of luminum, construction pper, nd the tble top) to drg the crts on. 1: Coefficient of Kinetic Friction To study nd clculte vrious coefficients of kinetic friction, we will use pulley system s shown in Figure 2(). The pulley ( smrt pulley ) is equipped with sensor tht llows you to mesure nd grph the velocity of the msses s function of time vi the Dt Studio softwre. With the velocity grph you cn obtin the ccelertion of the mss system by finding the slope of the pproprite liner fit, similr to the Atwood lb (lb 5). Looking t the free body digrms of our system (Figure 2(b)), we cn write Newton s second lw for ech mss s m 1 = T fr (3) m 2 = m 2 g T (4) Here we hve ssumed tht the ccelertions of the two msses re sme by neglecting ny frictionl effects on the pulley mking the tension in the string uniform. The kinetic frictionl force fr is given by fr = µ k F N = µ k m 1 g (5) 2

3 m1 FN T m2 fr m1 W1 T m2 W2 () (b) Figure 2: () Pulley system used to clculte u k. (b) Free body digrms for the pulley setup. W i is the weight of the object nd fr is the frictionl force. The system of equtions (Eqs. 3-4) cn be solved for the ccelertion in terms of the msses (m 1, m 2 ), g, nd µ k = (m 2 µ k m 1 )g m 1 + m 2 (6) Devise n experiment to clculte µ k for vrious surfces, mking use of the smrt pulley system, the friction crts, nd the different surfces. Tke mesurements with ll 3 crts (felt, plstic, nd cork) on one of the surfces. Use up to 3 different msses for ech crt. Remember to do severl trils for ech run to obtin consistent dt. 2: Coefficient of Sttic Friction To mesure the sttic coefficient of friction µ s we will use the force sensor. The force sensor records the pulling (or pushing) in Newtons vi the Dt Studio softwre. Connect the force sensor to one of the friction crts using string. With no force on the sensor press, the zero (tre) button before tking ny mesurements (this should only be performed once). Open the grph under the disply section in Dt Studio. With the force sensor setup nd ttched to the crt, strt to slowly nd crefully pull on the crt on of the surfces while monitoring the force vlue with the grph. You wnt to record the minimum force needed for the friction crt to brek wy nd strt moving. Your grph should look similr to Figure 1 (note: depending on the force sensor setup, your grph might be upside down!). Hve every member of the lb group try this. Repet this procedure for ll the friction crts (felt, plstic, cork) using t lest 5 different msses for ech crt. 3

4 3: Coefficient of Kinetic Friction by Force Sensor We cn check our µ k vlues obtined from the first experiment by mking use of the force sensor. Devise nd experiment to mesure the coefficient of kinetic friction using the force sensor. Record the force, norml force nd obtin µ k grphiclly. How do your vlues compre with those from experiment 1? Repet this experiment for the vrious crts with 3 different msses. Hint: This prt my be difficult t first, but drw free body digrm of the crt nd force sensor nd then convince yourself why you wnt the crt to move with constnt velocity (look t the velocity grph s guide). A full lb report is not necessry for this lb. Answer the questions on the following pge nd turn it in with your signed dtsheet. 4

5 PHYS 123, Lb 6 Questions Nme: CWID: Write your nswers on seprte sheet nd ttch your signed dtsheet when turning it in. You must show ll of your work for full credit. Mke it cler to me you understnd wht you re doing. Any grphs or tbles should be mde vi computer softwre nd ttched to this hndout. 1. Answer the following questions using the dt you cquired in this experiment: () For the first experiment, crete dt tble for the different msses (M 1, M 2 ), the ccelertion, nd the clculted coefficient of friction µ k. Remember to lbel the crt types (felt, cork, plstic) in your tble nd describe the surfce. (b) Do your mesured vlues of µ k mke sense? Compre them with smple coefficients of friction (for vrious mterils) found in your textbook. (c) For the second experiment, wht is the force tht you re mesuring? Crete plot of this mesured force vs the norml force of the friction crt. Find its slope nd explin wht it represents. (d) For the third experiment, mke dt tble consisting of the crt msses, ny pplied force, nd the norml force. Using your dt, crete grph tht represents the coefficient of friction. (e) How does your coefficient of friction from the third experiment compre with the one you obtined from the first experiment? Wht re the sources of error? 5

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