Procedure I Data Table 1: Mass and Weight Object Mass in g Mass in kg Weight in N Wooden Friction block 31.1 0.031 0.30 Glass /sandpaper friction block 55.6 0.056 0.55 50 g hanging mass 50 0.05 0.49 100 g hanging mass (assume known to 3 sig fig 100 0.100 0.980 500 g hanging mass (assume known to 3 sig fig) 500 0.500 4.90 Data Table 2: Dependence on Surface Area Total weight Trial 1 in N Trial 2 in N Trial 3 in N Average Applied Force (Kinetic) block plus 500 g flat 5.31 1.50 1.60 1.70 1.60 Applied Force (Static) block plus 500 g flat 5.31 3.00 3.10 2.80 2.97 Applied Force (Kinetic) block plus 500 g side 5.31 1.40 1.50 1.30 1.40 Applied Force (Static) block plus 500 g side 5.31 2.50 2.90 2.90 2.77 Coefficient of Kinetic Friction Flat 0.308 Average Coefficient Coefficient of Static Friction Flat 0.571 Kinetic 0.29 Coefficient of Kinetic Friction Side 0.269 Static 0.56 Coefficient of Static Friction Side 0.533 Procedure II Data Table 3: Dependence on Support Force Total weight Trial 1 in N Trial 2 in N Trial 3 in N Average Applied Force (Kinetic) block plus 100 g 1.28 0.30 0.30 0.30 ).30 Applied Force (Static) block plus 100 g 1.28 0.50 0.60 0.50 0.53 Applied Force (Kinetic) block plus 150 g 1.77 0.50 0.40 0.50 0.47 Applied Force (Static) block plus 150 g 1.77 0.80 0.80 ).80 ).80 Coefficient of Kinetic Friction (100g) 0.23 Average Coefficient Experiment Graph Coefficient of Static Friction (100 g) 0.41 Kinetic 0.3 Coefficient of Kinetic Friction (150g) 0.37 Static 0.52 Coefficient of Static Friction (150 g) 0.63Procedure III Data Table 4: Dependence on Surface material Total weight Trial 1 in N Trial 2 in N Trial 3 in N Average Applied Force (Kinetic) glass block plus hanging mass 5.45 0.90 0.90 0.90 0.90 Applied Force (Static) glass block plus hanging mass 5.45 1.00 1.00 0.90 0.97 Applied Force (Kinetic) sandpaper block plus hanging mass 5.45 2.50 2.40 2.30 2.40 Applied Force (Static) sandpaper block plus hanging mass 5.45 2.70 2.60 2.70 2.67 Applied Force (Kinetic) paper block plus hanging mass 5.20 1.00 1.00 1.00 1.00 Applied Force (Static) paper block plus hanging mass 5.20 2.40 2.50 2.50 2.47 Coefficient of Kinetic Friction glass 0.165 Coefficient of Static Friction glass 0.178 Coefficient of Kinetic Friction sandpaper 0.44 Coefficient of Static Friction sandpaper 0.489 Coefficient of Kinetic Friction paper 0.266 Coefficient of Static Friction paper 0.38 Procedure IV Data Table 5: Angle of repose Trial 1 Trial 2 Trial 3 Average Static Coefficient Max angle wood block 30 31 30 30.3 0.584352819 Max angle glass block 15 19 16 15.7 0.281087323 Max angle sandpaper block 35 36 31 34 0.674508517 Max angle paper block 30 25 28 26.7 0.502947603How did Surface Area appear to affect the coefficient of friction? How did the Support Force appear to affect the coefficient of friction? How did the Material appear to affect the coefficient of friction? How does the static coefficient determined using the spring scale compare to the value using the max angle of repose? Which do you think is more accurate?Do your experimental results support the statement that the coefficient of kinetic friction is smaller the the static coefficient for the same materials? If not, why do you think it didn't?4. Friction Purpose The purpose of this lab is to explore the force of iction What is Friction A force is a push or pull on an object, represented by a vector with magnitude and direction, caused by the interaction between two objects. The force of friction is a resistive force opposing motion between two objects in contact with one another. Friction is present any time two objects slide or attempt to slide against one another, such as when a skier slides down an icy slope, or a crate is dragged across the oor, or when a box is prevented from sliding down a ramp. The force of friction always acts parallel to the surface between the two objects, and its magnitude depends on several factors including the materials in contact with one another and the support force (S) between the two objects. The magnitude of the applied force attempting to set one of the objects in motion also inuences what is known as the static iction force when the objects are not moving relative to one another. When the objects are moving relative to one another, neither the magnitude of the applied force, nor the speed of the moving object affects the magnitude of what is known as the kinetic friction force. See Figure lbelow. Support Force Acceleration 4 Applied Force Figure 1 Force Diagram example A few notes about free body diagrams. A free body diagram shows all the forces acting on a single object. The \"force\" arrows always act at the center (center of mass technically) of the object. In Figure 1 above there are four forces acting on the blue box. The Support Force and the Weight are equal in magnitude but opposite in direction. Notice the length of the two arrows are the same to indicate the same magnitude. The Applied force to the left is longer than the F orcc of Friction to the right, so there is a net force acting to the left. This net force results in an acceleration to the left as shown by the acceleration arrow. Sometimes friction is benecial, such as when it helps to hold a car on course during a turn. Other times friction is detrimental and should be minimized to improve the efciency of a specific operation, such as within an internal combustion engine, or in sports like skiing, ice skating, bowling and curling. 4. Friction Types of Friction There are two main types of friction, static and kinetic friction, depending on how the interacting objects are moving relative to one another. Static friction exists between two objects that are not moving relative to one-another even though an applied force acts to attempt to cause motion, and can have a range of magnitudes. The magnitude of the static friction force increases proportionally to the applied force up to some maximum value. For values of the static friction force less than the maximum force, there is no universal equation used to define the magnitude; it is simply equal to the applied force. Remember this is a result of Newton's first law; an object at rest remains at rest unless there is a net force.... Since the object remains at rest the magnitude of the force of friction and the applied force must be equal: fs = Fapp Where: fs is the magnitude of the force of static friction and Fapp is the magnitude of the applied Force. The maximum static friction force, however, is the maximum force that can be applied before the object starts to slip along the connecting surface. The equation for maximum static friction force is : fs, max = UsS Where: fs,max = maximum static friction us = coefficient of static friction S = magnitude of the support force The coefficient of static friction is dependent upon the materials in contact with one another and is determined experimentally. The lower the value of the coefficient of static friction between two materials, the easier the objects slide against one another and the smaller the maximum force of static friction is between them. The larger the support force is between two objects, the larger the maximum static friction force. A full description of the static friction force including all the conditions discussed above is represented by the equation: fs SUSS4. Friction Once an object starts to slide along the surface of another object, the friction force between the objects becomes the force of kinetic friction. The force of kinetic friction is also parallel to the interacting surface, and points in the opposite direction of the motion. However, it s smaller than the maximum static friction force, and does not change as the applied force changes. The force of kinetic friction is represented by the equation: fl = MKS Where: fx = magnitude of kinetic friction MK= coefficient of kinetic friction = magnitude of the support force The coefficient of kinetic friction for two materials is always smaller than the coefficient of static friction for the same two materials, so it is easier (requires less force) to keep an object moving than to start the object moving from rest. The force of friction as compared to the support force is represented by the diagram in Figure 2 below 6.0 HS kinetic friction Force (N) HK -1.0 static friction 0.0 - Time (s) *- 10.0 Figure 2 applied force vs time The friction force is independent of the surface area of interaction between two objects. For example, a rectangular object stood on its end (small surface area) requires the same amount of applied force to slide at constant speed across a surface as when resting on its side (large surface area. See Figure 3 below4. Friction AppliEd force A lied force Friction Figure 3 Friction vs surface area Causes of Friction Friction is caused by the interactions of microscopic molecules at the surface of two interacting objects. The surfaces of even the smoothest materials are irregular when observed at the molecular level. Most spikes or peaks at the surface of one object do not line up with the peaks of the surface of an object they are in contact with, creating very few actual physical connections. Smooth surfaces tend to have fewer points of contact on a molecular level than rough surfaces. Molecular bonds form where the surfaces do touch. These bonds must be broken to move the object, causing the resistive static friction force. Once the bonds are broken and the object is moving, the bonds cannot reform but attraction remains between the closest points of contact of the two objects, causing the smaller kinetic friction force. Figure 4 Friction up close 4. Friction Methods for Measuring Friction Forces and Coefficients Kinetic Friction The Kinetic friction force, and subsequently the coefficient of kinetic friction, can most easily be determined by measuring the applied force when an object is moving in a straight line at a constant speed and therefore not accelerating. Remember Newton's Second Law states that the acceleration of an object is directly proportional to the NET force, so if the acceleration is zero (constant speed), then the NET force is also zero. Once again there are four forces acting on the object, gravity which must be equal in magnitude but opposite in direction of the support force, and the applied force which must be equal in magnitude but opposite in direction of the kinetic force of friction. Remember this is only true when it is moving at constant velocity. fl: = Fapp We also know the Kinetic friction force is only dependent upon the support force fk. = M5 Combining these two equations we see that lukS = Fapp Rearranging Farr #1: 5 Static Friction The static friction force can be determined by similarly measuring the maximum applied force the object can sustain before sliding. Again, because the object is at rest, the Applied Force must be equal in magnitude but opposite in direction of the Force of static Friction. =F amax app f5,max = nus-S 4. Friction Combining the two equations we see that #55 = Fapp Rearranging: F as = (1513p Another way to determine the coefficient of static friction can be determined om the maximum angle of repose. The angle of repose is the angle at which an object rests on an inclined surface. The maximum angle at repose is the largest angle [or which the obiect remains at rest. See Figure 5 below: Figure 5 Free Body Diagram of an object on an Incline Don't worry about the trig functions, the worksheet will automatically calculate the trig functions for you. Once again, we use Newton's second law that states an object at rest must have a zero Net Force. If we use the slope as our coordinate system, this means the forces parallel to the surface of the incline must be equal in magnitude but opposite in direction. There are only three forces acting on the object, the weight acting downward, the support force pointing upward perpendicular to the surface and the force of friction which is pointing up the slope. If we write the force of gravity in two components, one along the direction of the incline and one perpendicular to the incline we can use Newton's second law. These two components are shown in dashed arrows in Figure 5 above. That means when the angle is set at the maximum angle just before the object begins to slide, the forces parallel to the surface must be equal in magnitude: f5,max : mg Sll'l 9mm: AND... the forces perpendicular to the surface of the incline must also be equal in magnitude 5 : mg cos 9],,\"- 4. Friction Procedure I Dependence of Friction on Surface Area 1. Gather the materials listed above 2. Place the wooden board on a at surface. 3. Determine the mass of the following objects using the digital scale and record the mass to the nearest 0.1 g in Data Table l in the worksheet 0 Wooden friction block (from the friction block set) 0 Glass /sandpaper friction block (from the friction block set) 0 50 g hanging mass 4. Convert the above masses to kg using the conversion factor 1 kg = 1000 g. Ihave converted the mass of the 100 g and 500 g hanging masses (assumed to be exact since the digital scale will not record masses this large) 5. Calculate the Weight of the above objects using the equation W=mg= m*9.81 m/sz. Record to the nearest 0.01 Newton's in the worksheet. (I have completed this for the 100 g and 500 g hanging masses) 6. Place the plain wooden block from the friction block set on the plain wooden block at on the wooden board near one end. See Figure 6 below Figure 6 Friction block on grooved board 7. Lightly mark the top side of the friction block not in contact with the wooden board for later reference. 8. Place the 500 g hanging weight on top of the friction block. Calculate the sum of the Weights of the 500 g hanging mass and the friction block. Enter this in Data Table 2 in the worksheet. Be sure you are entering the Weight (in N) and not the mass (in g). This value will automatically populate the three rows below this value. 4. Friction 9. Zero the 500 g spring scale for horizontal use by letting the scale rest at and adjusting the metal tab until the scale reads zero. See Figure 7 below. Figure 7 Zeroing the spring scale 10. Connect the spring scale to the wood block via the hook on the block. 11. Using the spring scale, slowly pull the block along the horizontal board. Try to pull the block at a steady speed, and read the force on the scale as you pull. Record the smallest force indicated on the scale that allows the block to move with constant speed as the force of kinetic friction to 0.01 Newtons in the worksheet. It is important you try to pull the block at a constant speed. NOTE: the scale should be held horizontally and should not touch the surface of the wooden board while the block is being pulled as shown in Figure 8 below. Figure 8 Setup with spring scale above the board 12. Repeat Step 11 for two additional trials. Note: For each trial, begin the measurement from the same location and make certain that the block is sliding over the same path at a constant speed on the wooden board. 4. Friction 13. Calculate the Average of the three Trials and enter in Data Table 2 in the worksheet. Record these values to 0.01 Newtons in the worksheet. 14. Place the block at the same starting position with the marked side up. This time you are trying to pull the spring without moving the block... Very gradually increase the force until the block nally moves. Carefully observe the spring scale as you begin pulling on the scale. Record the force required to initiate movement of the block as the force of static friction to 0.01 Newtons in the worksheet. Try this a few times before you start recording. Very slowly increase your pull and watch the scale very carefully. As soon as the block starts moving the scale reading will reduce. You are looking for the value just at the moment the block moves. Note: The force of static friction should be slightly larger than the force of kinetic friction. If you do not observe this, repeat the trial and pay close attention to the position of the scale when the block initiates movement. It may take some practice to correctly read the scale at the correct time. 15. Repeat Step 14 for two additional trials recording in Data Table 2. 16. Calculate the average of the three Trials and record these values to 0.01 Newtons in Data Table 2 in the worksheet. 17. Position the wooden friction block on its side and balance the 500 g mass on top. See Figure 9 below Figure 9 Setup with block on its side 18. Repeat steps 10-16 for the block in this position. 19. Calculate the coefcient of static and kinetic friction for the at block and the block on its side using the corresponding average friction forces calculated in Step 18. _ Fapp _ Pam: .us _ S I \"It _ S 4. Friction Remember the support force is equal to the total Weight (due to Newton's second law). Record these values in the worksheet, Data Table 2. Calculate the average of the coefficient of kinetic friction on the Flat and Side and enter it into the Data Table 2. Repeat for the Static Coefficient. Procedure II Dependence of Friction on the Support Force . Return the friction block to the flat side with the marked side up at the starting position on the wooden board. Place the 100 g hanging weight on the friction block and record the total weight to 0.01 Newtons in Data Table 2 in the worksheet. 21. Repeat Steps 10-16, recording the measurements in the worksheet. 22. Return the friction block to the starting position with the marked side up on the wooden board. 23. Place the 50 g hanging mass and the 100 hanging mass on top of the friction block and record the total weight of the hanging masses and friction block to 0.01 Newtons in Data Table 3 in the worksheet. 24. Repeat Steps 10 through 16, recording the measurements in the worksheet. 25. Calculate the coefficient of static and kinetic friction for each weight using the average friction forces recorded in Data Table 3 and record to the 0.1 precision in the worksheet. 26. Calculate the average coefficient of static and kinetic friction (by averaging the coefficient for the 500, 100 and 150 g coefficients) (Be sure to include the 500 g value from Data Table 2)and record to 0.01 precision in the worksheet. 27. Create a graph of average static friction force on the vertical (y) axis versus the support force on the horizontal (x) axis using Excel and the steps used in the previous lab. Include the point (0,0) in your data. Include a graph title, axes titles with units, and a linear trendline with the equation shown. Use Excel's copy and paste feature to copy your graph onto the worksheet. Add the static friction coefficient determined from the trendline to 0.01 precision in the worksheet 28. Repeat step 27 for the kinetic friction force, copy the graph into the graph #2 box in the worksheet. Procedure III Dependence of Friction on Surface Material 29. Choose the weight for the friction block that produced the most consistent results in procedure II. 30. Record the total weight of this block and the chosen hanging mass from step 29 to 0.01 Newtons in Data Table 4 in the worksheet.4. Friction Procedure IV Max angle of incline 40. Place the wooden friction block on the wooden board in the starting position with the same side down as was used in Part 1 and Part 2. 41. Slowly raise one end of the wooden board until the friction block just starts to slide. Hold the board at this angle and measure the angle of incline with the protractor, see the gure below. Record the angle to 0.1 degree in the worksheet. (Notice on the picture below, when the wood ramp is horizontal the string should read 90. To read the angle you determine the difference between the angle shown and 90". For example in Figure 11 below the string is showing 108", so the angle would be 108 7 90 =180 Figure 11 Setup with protractor to measure angle 42. Repeat step 41 for two additional trials, recording the measurements in the worksheet. 43. Place the friction block with the glass surface glass side down in the starting position on the wooden board 44. Repeat steps 41 and 42 for the glass surface 45. Place the friction block with the sandpaper surface sandpaper side down in the starting position on the wooden board 46. Repeat steps 41 and 42 for the sandpaper surface 47. Place the friction block with the paper surface paper side down in the starting position on the wooden board 48. Repeat steps 41 and 42 for the paper surface 49. Calculate the average maximum angle of repose found for each of the four surfaces and record these average to 0.1 degrees in the worksheet. 50. The coefcient of static 'iction will be auto populated using the equation: as = tan 6mm: for each of the four surfaces. 4. Friction 51. Answer the questions on the spreadsheet. Be sure your entire answer is visible in the box (you can increase the row height if your answer doesn't fit) 52. Return all items to your kit