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 4.904. Friction Purpose The purpose of this lab is to explore the force of friction 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 friction 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 Friction 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 Force 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 specic operation, such as within an internal combustion engine, or in sports like skiing, ice skating, bowling and curling. 4.1 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 dene the magnitude; it is simply equal to the applied force. Remember this is a result of Newton's rst 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: f: : Fapp Where: fS is the magnitude of the force of static friction and Pam 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 : \"33 Where: Em\" = maximum static friction jug = coefcient of static friction S = magnitude of the support force The coefcient of static friction is dependent upon the materials in contact with one another and is determined experimentally. The lower the value of the coefcient 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: is Sans-SI 4.2 4. 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 is 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: fk = MKS Where: fk = magnitude of kinetic friction MK= coefficient of kinetic friction S = 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 below 4.34. Friction ADDIiEd 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 4.4 4. Friction Methods for Measuring Friction Forces and Coefficients Kinetic Friction The Kinetic friction force, and subsequently the coefcient 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 ft 2 MRS Combining these two equations we see that #199 = Fapp Rearranging Farm? Mk - 3 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. fs,max = Fapp fsmax = #33 4.5 4. Friction Combining the two equations we see that #55 = Fapp Rearranging: F #3 2 (:31? Another way to determine the coefcient of static friction can be determined from the maximum angle of repose. The angle of repose is the angle at which an object rests on an inclined surface. The maximum angle of 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: fsmax : m9 Sin 9mm: AND... the forces perpendicular to the surface of the incline must also be equal in magnitude 5 = mg cos Om\". 4.6 Procedure II Dependence of Friction on the Support Force 20. 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 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 0.30 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 0.80 0.80 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) 0.63PHOTO # 1 insert copy of static friction graph PHOTO # 2 insert copy of kinetic friction graph