Experimental Objectives FRICTION The purpose of this experiment is to investigate how (a) the coefficient of kinetic friction and (b) the coefficient of static friction between given pairs of surfaces depend on the normal force between the surfaces, the area of contact between the surfaces. Apparatus Photogate Balance Friction Block w/ hook Super Pulley w/ Clamp Mass and Hanger Set String Universal Table Clamp Track System Overview When an object is at rest on a surface, any attempt to move the object will be opposed by a force of friction. For these surfaces in contact, the magnitude of the force of friction f is proportional to the load or normal force (F n ) on the object and is given by: f = µ F n The constant of proportionality, µ, is the coefficient of friction. When a force F is exerted on the block in a direction parallel to the surface and no motion occurs, the applied force is balanced by the force of static friction f s exerted on the object by the surface and acting opposite to the possible direction of the object s motion. The smallest magnitude of the applied force necessary to set the block in motion is the maximum force of static friction, given by: f = µ F s s n The constant of proportionality, µ s, is the coefficient of static friction. When the applied force is greater than the maximum force of static friction, the object slips or slides and is set into motion. While in motion, the object is retarded by the force of kinetic (or sliding) friction, f k : f = µ k k F n A block of mass M 1 is placed on a level track surface and connected by a string to a mass (m 2 ) hanging over a pulley. As the mass (m 2 ) is released and starts to fall, the block (M 1 ) will slide across the table. Using the Photogate/Pulley System, students will measure the velocity of an accelerating block and determine the acceleration of the block from the graph display. The theoretical values of the coefficient of kinetic friction will be calculated from the results obtained. With this experimental setup, students will investigate the effects of changes in surface area and mass (normal force) on the coefficients of friction. By carefully inclining the surface, the coefficient of static friction will also be determined from the limiting angle of 2003 Martin O. Okafor [revised from PASCO Manual] - 1 - rev.6/13/03
repose, the angle of inclination at which the block just begins to slide on the inclined plane. In determining the coefficient of kinetic friction, the system slides at a constant acceleration, as shown by the velocity-time graph plotted by the DataStudio software. From the equations of motion for this system, it can be shown that the coefficient of kinetic friction can be determined from the following equation: mg 2 ( M1+ m2) a µ k = Mg 1 (1) PROCEDURE: P1: Computer/Photogate Setup 1. The ScienceWorkshop interface and the computer should be already switched on. 2. Connect the Photogate s phone plug to Digital Channel 1 of the interface. 3. Launch DataStudio and open the activity under PHYS_2211L/Friction. Doubleclick on document titled as shown: DataStudio P21 Kinetic Friction.DS The DataStudio document should open with a graph display of Velocity versus Time. P2: Sensor Calibration and Equipment Setup 1. Place the wooden friction board on a horizontal surface and check to ensure that the board is level. 2. Attach a super pulley to the right end of the board. Use the three-legged rod and clamp to mount the Photogate so that it is suspended above the pulley. 3. Measure the mass of the Friction Block. Record the mass in the Data Table in the Lab Report section. 4. Use a piece of string that is about 10 centimeters longer than the distance from the top of the horizontal surface to the floor. Attach one end of the string to the block. 5. Put the string in the groove of the pulley. Attach the mass hanger to the other end of the string. Set up the block and Pulley as shown, with the string parallel to the board. 2003 Martin O. Okafor [revised from PASCO Manual] - 2 - rev.6/13/03
6. Ensure that the surfaces of both the horizontal surface and the block are clean, dry and free of dirt and grit. Wipe the contacting surfaces of the block and the cart with a clean damp (not wet) paper towel and dry these surfaces with a dry paper towel. It is extremely important that you keep these surfaces clean and do not touch them with your bare hands. The accuracy of your data depends on the condition of these surfaces. Use the same section of the horizontal cart for the motion of the block through the experiment for consistency of conditions. P3: Coefficient of Static Friction Wide, Smooth Surface 1. Place the block with its largest smooth side on the horizontal surface. 2. Gently place some masses on the mass hanger and gradually increase the load until the block just begins to move on the surface without needing an initial push. Measure and record the value of the TOTAL hanging mass (remember to include the mass of the hanger) in Data Table #1. 3. Place a 100 g mass on top of the block and increase the mass on top of the block in increments of 100 g up to a total of 400 g on the block. 4. Calculate the values of the normal force and the force of static friction f s for each data set in Data Table #1. P4: Coefficient of Kinetic Friction Wide, Smooth Surface 1. Using the same setup as in Procedure P3 above, place the block with its largest smooth side on the horizontal surface. 2. Gently place some masses on the mass hanger so that the block slides on the surface without needing an initial push. Measure and record the value of the TOTAL hanging mass (remember to include the mass of the hanger). 3. Move the block away from the pulley until the hanging mass is almost up to the pulley. Note the position of the edge of the block as the starting point for the block for the data runs in this procedure. Hold the block in place. Turn the pulley so the 2003 Martin O. Okafor [revised from PASCO Manual] - 3 - rev.6/13/03
photogate s beam is not blocked (light-emitting diode on the photogate is not lit). 4. Begin data recording. 5. Release the block. 6. Stop data recording before the block hits the pulley. Do not let the block hit the pulley. The data will appear as Run #1. 7. Place a 100 g mass on top of the block and increase the mass on top of the block in increments of 100 g up to a total of 400 g. Repeat the previous steps #3 through #6 for each total set of masses placed on the block. 8. Measure and record the total mass of the block and additional mass in the Data Table #2 for every data run. Analyzing the Data 9. Determine the experimental acceleration for each of the data runs. 10. Click in the Graph display to make it active. Find the slope of the velocity vs. time plot, the average acceleration of the block. In DataStudio, select Run #1 from the Data Menu ( ) in the Graph display. If multiple data runs are showing, first select No Data from the Data Menu and then select Run #1. Click the Scale to fit button ( ) to rescale the Graph axes to fit the data. Next, click the Fit menu button ( ). Select Linear. Record the slope of the linear fit in the Data Table #2 in the Lab Report section. Repeat the above procedure for each of the remaining data runs. 11. From the total mass values and the value of the acceleration, the coefficient of kinetic friction for each data run in the Data Table #2 should be calculated and recorded. P5: Coefficient of Kinetic Friction Different Surface Area 1. Remove the additional mass from the block and from the mass hanger to return the block and mass hanger to their original state from Procedure P4. 2. Turn the block on its side so that its smallest smooth side is on the horizontal surface. 3. Place a 400 g mass on top of the block and repeat steps #3 through #6 as in Procedure P4. 4. Record data in Data Table#3. 2003 Martin O. Okafor [revised from PASCO Manual] - 4 - rev.6/13/03
P6: Coefficient of Static Friction The Limiting Angle of Repose 1. Set up the cart as an inclined plane and measure the angle of inclination with an inclinometer placed on the surface of the cart. 2. Place the block so that its largest smooth side is on the inclined surface and gradually lift the upper end of the inclined cart until a certain angle of inclination is reached when the block just begins to slide down. 3. Measure this angle of inclination using the inclinometer. With the inclinometer held on the inclined cart, carefully note the precise angle at which the block begins to slide from the previous starting point on the cart as in Procedure P4. This is the limiting angle of repose, θ max. 4. Repeat and record the angles determined for any three trials in Data Table #4. 2003 Martin O. Okafor [revised from PASCO Manual] - 5 - rev.6/13/03
Lab Report Section DATA Weight of block = Weight of mass hanger = P3: Coefficient of Static Friction Wide, Smooth Surface Data Table #1: Total mass Total mass Normal force Force of Static on block on hanger (N) Friction (N) 0 g 100 g 200 g 300 g 400 g Coefficient of Static Friction, µs, from graph = P4: Coefficient of Kinetic Friction Wide, Smooth Surface Data Table #2: Procedure P4 Run #1 Run #2 Run #3 Run #4 Run #5 Total mass on block 0 g 100 g 200 g 300 g 400 g Total mass on hanger aexp acceleration (m/s 2 ) Averages: µk coefficient of friction Deviation P5: Coefficient of Kinetic Friction Different Surface Area Data Table #3: Procedure Total mass on Total mass aexp µk P5 block on hanger acceleration [on side, (m/s narrow edge] 2 coefficient of ) friction Run #6 2003 Martin O. Okafor [revised from PASCO Manual] - 6 - rev.6/13/03
P6: Coefficient of Static Friction The Limiting Angle of Repose Data Table #4: Trial Limiting angle µs of repose, coefficient of Deviation θ max static friction #1 #2 #3 Averages: CALCULATIONS 1. From the data of Procedure P3, plot a curve using the values of the total normal force as abscissas and the values of the force of friction as ordinates. From the best line of fit through the data points on this graph, obtain the coefficient of static friction, µs, for the wood on the metal (cart). Record µs on the data sheet. 2. Derive Equation (1), as given in the Overview, for the coefficient of kinetic friction when the block slides with a constant acceleration. Include your derivation on a separate sheet in your Lab Report. 3. From the values of the acceleration in Data Table #2 from Procedure P4, compute the coefficient of kinetic friction, µk, for each data run in the table. Calculate the average value of µk, the deviation for each data run, and the a.d. (average deviation). Record your result on the data sheet. 4. From the data in Table #3 from Procedure P5, calculate the coefficient of kinetic friction for the case of the block on its (narrow) side. Record your result and compare it with the value of µk obtained from Procedure P4 by finding their percent difference. 5. From the data in Table #4 from Procedure P6, calculate µs for the wood on the metal cart for each of the three trials and obtain an average value, the deviation for each trial, and the a.d. (average deviation). Record your result on the data sheet and compare it with the value of µs obtained from the graph in Procedure P3 by finding their percent difference. 2003 Martin O. Okafor [revised from PASCO Manual] - 7 - rev.6/13/03
QUESTIONS 1. Explain in your own words why you must be very careful when placing additional masses on the hanger in Procedure P3 to find when the block just begins to slide without any initial push. 2. How does the coefficient of friction vary when the mass of the block was increased (thereby increasing the normal force)? 3. When the mass of the block is increased, does the force of kinetic friction increase? Why? 4. How does the coefficient of kinetic friction vary with the area of contact between the block and the horizontal surface? Is there any significant difference between the coefficient of kinetic friction determined when the block was placed on its largest side or when it was on its narrow side? 5. When the area of contact between the block and the horizontal surface is increased, does the force of kinetic friction increase? Why? What is the implication of this result in designing the widths of automobile tires? 6. Using the average value of the limiting angle of repose in the Data Table #4 from Procedure P6, and the value of the coefficient of kinetic friction from Procedure P4, calculate the acceleration of the block after it begins to slide down the incline in Procedure P6. 2003 Martin O. Okafor [revised from PASCO Manual] - 8 - rev.6/13/03