Friction Laws and Work-Energy with Non Conservative Forces

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Part C: Direct Measurement of the Kinetic and StaticFrictional ForcesThe kinetic and static frictional forces can be measureddirectly using the force sensor as shown in Fig. 2. Forces to bemeasured are applied to the hook located at one end of theforce sensor. Connect the force sensor to channel A. Click onthe icon for Analog Channel A and select the force sensor (notthe student force sensor) from the list of available analogsensors and set the sample rate to 1000 (hz).• Calibration of the Force Sensor: The force sensor works bymeasuring the bending of a metal strip by the force applied toit. In order to measure forces accurately the sensor must firstbe calibrated.• Click the calibrate sensors tab and select the two pointcalibration. In the Calibration Point 1 area enter the value ofzero in the Standard Value Box. In the Calibration Point 2area enter the value of 10.29 in the Standard Value Box.• In the following steps you must hold the force sensor atrest in a vertical position. With nothing connected to theforce sensor press the TARE button on the sensor and thenclick on the Read from Sensor Button in the CalibrationPoint 1 area.• Press the TARE button againwith nothing connected to theforce sensor. Add an additionalmass of 1.00 (kg) to the masshanger for a total mass of 1.05kg (corresponding to a totalgravitational force of 10.29 N).Holding the force sensorvertically, connect the masshanger to the force sensor’shook and then click on the Readfrom Sensor Button in theForcestaticf s(max)kineticDirect MethodFig. 4timeCalibration Point 2 area. Finally click OK to exit thecalibration procedure.• Click on the Sampling Option tab and select a data collectiontime of 10 seconds and open a plot window to display theforce.• It is important to verify that the force sensor is workingcorrectly. Holding the force sensor vertically with nothingconnected to it, press the TARE button and collect data for afew seconds and then connect the hanger with the 1.00 (kg)added mass to the force sensor. The graph should indicate anet force of zero while nothing was connected and 10.3 (N)with the hanger and added 1.00 kg mass connected. If you donot obtain these values you need to repeat the calibrationprocess. Include a copy of the calibration plot with yourreport.• Attach a short string between the hook on the force sensorand the block which should be placed on the plank with thewood side down. Place masses on top of the block so that thetotal mass of the block plus added masses is about 1.5kilogram.• Press the TARE button on the force sensor with no forceapplied and then pull horizontally on the force sensor to applya force to the block. Begin with a very small force and veryslowly increase it until the block begins to move. Continue topull with the reduced force required to keep the block movingmore or less uniformly without accelerating. The graph of theapplied force versus time may be similar to Fig. 3.• The maximum force applied just before the block moved isthe maximum force of static friction f s(max) while the meanvalue of the force as the block moves with a constant speed isthe force of kinetic friction. Using the Smart Tool find f s(max)and f k . Determine the coefficients of static and kinetic frictionusing Eq. 2 to compute the normal force and Eq. 3 to obtainthe coefficients of friction.• Do a few more trials and obtain mean values and standarddeviations for the coefficients of static and kinetic friction.• Comment on the relative values of μ s and μ k .• Compare your values of μ k obtained using the two differentmethods of Part A and Part C. Assume the error in eachmethod is twice the standard deviation. Taking these errorsinto account are methods "A" and "C" consistent? However,the standard deviation is only a measure of random errors anddoes not include any systematic errors in the experiment.Part D: The Force of Rolling FrictionIntroduction: When the wheel of a car moves along a flatroad it will experience a kinetic frictional force if the wheel isslipping. If the car is speeding up or slowing down withoutslipping (or even moving with a constant velocity against anair resistive force) astatic frictional force actson the wheel. In additionto these frictional forcesthere is a third type offrictional force known asrolling friction. Rollingfriction between asurface and a wheel isθdue to deformation of the surface and the wheel itself andadhesion (stickiness) of the surfaces. As deformation of theflat surface and the wheel occur, a resistive force developssince the wheel has to “plow its way” through the surface.The resistive rolling frictional force follows an empirical lawthat is the same as for kinetic friction:froll= μ FrN...( 8)where μ r is the coefficient of rolling friction. The coefficientof rolling friction is usually much smaller than the coefficientof kinetic friction. For example, the coefficients of kinetic androlling friction for a steel railway car wheel on a steel rail areapproximately 0.2 and .001 respectively.Experimental: In this part of the experiment the coefficientof rolling coefficient of friction is measured for a cart. Thevalue obtained includes the rolling friction at each wheel asf rollF NmgmgcosθRolling FrictionFig. 5mgsinθ
well as any kinetic friction in the wheel bearings. Since therolling frictional force is very small, we should minimize thecontribution of other forces, such as gravity, that would tendto obscure the rolling frictional force. Ideally the plank shouldbe level to eliminate the gravitational force component.However, if the plank is not perfectly level, a smallgravitational force component will act on the cart in adirection parallel to the plank. We remove the possibleinfluence of gravity by measuring the acceleration of the cartfor motion in both directions. The cart is placed on the plankalong with the motion sensor and given a gentle push. Theacceleration is measured a few times. Then the cart is pushedin the opposite direction and its acceleration measured. Fromthese values we can obtain the coefficient of rolling frictionfor the cart.The cart is shown in Fig. 4. We have assumed that the tabletop may be tilted by a very small angle θ from the horizontal.When the cart is given a gentle push to the right we let itsacceleration be “a r ” and we choose the positive direction to betowards the right. The gravitational force component“mgsinθ” is smaller than the frictional force and the cart slowsdown even though it may be going down a slight hill. Weapply Newton’s II Law to the free body diagram shown:() 9FN= mg cosθ...mg sinθ− f = marollr...( 10)When the cart is pushed to the left we take the positivedirection to the left and both the frictional and gravitationalforces slow the cart down:− mg sinθ− f roll= mal...( 11)We solve equations (10) and (11) for the force of rollingfriction:froll− m ar=2( + a )l...( 12)• Place the motion sensor to the left of the cart and give thecart a gentle push to the right. Use the motion sensor to recordits velocity for three seconds. Do a linear fit to find theacceleration of the cart. Obtain at least three measurements ofthe acceleration “a r ” and find the average value. Note that thisvalue should be negative.• Place the motion sensor to the right of the cart and push thecart gently to the left and obtain at least three values of theacceleration “a l ”. Find the average which should also benegative.• Compute the coefficient of rolling friction of the cart usingEq. 13.How does the coefficient of rolling friction of the cartcompare with the coefficient of kinetic friction of the slidingblock?Check List: Minimal Requirements for Lab Notebook ReportThe significance of each graph must be discussed and the fitted values(such as the intercept and slope) must be compared with model valueswhen possible.Part A: Excel Data Table with masses used, calculated normal force,calculated frictional force and the coefficient of kinetic friction. Plot of kinetic frictional force versus the normal force with a linearfit through the origin. The % difference between the coefficient ofkinetic friction from the graph and the mean table value. Copy of one Data Studio plot of speed versus time.Part B: A copy of a few rows of your excel sheet displaying the distance,speed and energies. Plot of the kinetic, potential and total energy versus distance with alinear fit of the total energy curve. The value of the coefficient of kinetic friction obtained from the fit.Part C: Data Studio plot of the force applied by the force sensor versus time. The maximum force of static friction and the mean force of kineticfriction obtained from this plot. The coefficients of static and kinetic friction found from the abovefrictional forces. Compare the mean frictional force found in C with mean value foundin A and the value obtained in B. Discussion of these results.The coefficient of rolling friction is:μrollf=FrollN( a + a ) − ( a + a )−r lr= ≈2gcosθ2gl...( 13)Part D: Excel data table for measured accelerations and the computed valuefor the coefficient of rolling friction. Discussion.ConclusionsSince θ is a very small angle its cosine is very close to one.
Page 1 and 2: D. ShawVillanova UniversityMay 8, 2
Page 3: the motion sensor release the block

Friction Laws and Work-Energy with Non Conservative Forces

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