Kinetic & Static Friction When two objects touch, they exert forces on each other through surface contact. Frictional forces are contact forces that act parallel to the two surfaces, opposing any sliding of the surfaces. We often think of friction as a nuisance, but without it we could not walk, drive, or even pick up our food. The kitten does not fall because the force of friction between its fur and the couch cushions is equal and opposite to its weight. The polar bear slipped because the force of friction between the ground and its feet was too small. The ultimate source of these contact forces is the electrical nature of the atoms and molecules that compose the surfaces. The electrons and ions in any material attract or repel other matter that is brought in close proximity, even when the materials are electrically neutral. The result of these microscopic attractions or repulsions are macroscopic forces that we can feel. There are many different types of frictional forces static friction, sliding friction, rolling friction, fluid friction, and others. But they all have in common the tendency to resist sliding between two surfaces. The direction of these forces is always along the surface and opposite to any relative motion between the surfaces. The magnitudes of these forces depend on the character of the surfaces involved, and on how strongly the surfaces are pressed together. In this lab, you will inquire into the nature of the two most commonly encountered frictional forces:
Kinetic friction, F K, This operates when two surfaces are sliding relative to each other. It is always directed opposite to the relative motion, tending to decrease the relative velocity. Static friction, F S, operates when two surfaces are at rest relative to each other. It works to hold two surfaces bonded together and resists external forces to prevent relative motion. Our overall objectives will be to determine the magnitude of these frictional forces, and to develop empirical force laws for static and kinetic friction. As part of this we will: develop a method for measuring kinetic & static friction forces; determine the magnitudes of typical frictional forces; determine the relationship between load and friction forces; determine the effects of surface area; and compare the effect of different materials. A convenient way to evaluate frictional forces is to define a coefficient of friction in this way: Coefficient of Friction = Frictional Force / Normal Force The normal force is the component of the contact force between the two surfaces that is perpendicular to the surface. It is often called the load. A coefficient of friction is a unit-less number the ratio of two forces. It tells you how strong the frictional force is compared to the load on the surfaces. We use the Greek letter mu (μ) for frictional coefficients, with a subscript to indicate the type of friction: μ K for the coefficient of kinetic friction and μ S for the coefficient of static friction. Coefficients of friction depend on the materials in contact and vary with different conditions. The coefficient of friction between your feet and ice is much less than the coefficient between your feet and concrete; the coefficient between your tires and a wet road is less than that for a dry road. Typical values for coefficients of friction between many materials under many conditions have been measured and tabulated. (See Handbook of Chemistry and Physics in the lab.) However, these tabulated values are only average values; actual values can vary widely because no two pieces of material are exactly alike.
Experiment 1: Force of Kinetic Friction, Wood on Wood In the illustration above, a weighted wood block is connected by a string to a mass hanger with hanging masses, so that the string pulls on the block. You will add sufficient mass to the hanger so that the block starts sliding from rest. Objectives A. Find the strength of the kinetic friction force for several loads on the block. B. Determine how the coefficient of kinetic friction varies with varying loads. 1. Analyze the forces on the sliding block-hanging mass system and find a way to measure the frictional force on the block, F K. Draw a Free Body Diagram for the forces on the sliding block. Use a coordinate system in which the positive x-axis points along the string: +y Block: Mass 1 +x Referring to your FBD, write out ΣF x = ma x (Newton s 2 nd Law of Motion) for the block. Assign variable names for the forces, and be sure to account for their directions. Specify the mass of the block as m 1 and its acceleration as a 1x.
Draw a Free Body Diagram for the forces on the hanging mass. Use a coordinate system in which the positive x-axis points along the string: (The x-direction is downward in this case.) Mass 2 +y +x Referring to your FBD, write out ΣF x = ma x for the hanging mass. As before, assign variable names for the forces, and be sure to account for their directions. Specify the mass as m 2 and its acceleration as a 2x. Add the two expressions to find a single expression for the system. The left side will be the net force on the system in the x-direction, and the right side will be the mass of the system times the acceleration of the system, since a 1x = a 2x = a x, where a x is the acceleration of the system. Solve the expression for F K, the force of kinetic friction on the sliding block. Considering the expression you have derived, plan your experimental procedure: what do you need to do, and what do you need to measure, to find the magnitude of the frictional force on the block? Now consider a modified method. Instead of having the block start from rest, suppose you arrange it so that the block moves at constant speed after having been given a small push. Refine your expression for F K for this case. Plan what the experimental procedure must be for the block to move at constant speed. 2. Find an expression for the coefficient of kinetic friction between the plank and the block. Looking at your FBD, decide how you can determine the normal force, F N, between the block and the plank. Apply the definition of the coefficient of kinetic friction (μ K = F K /F N ) to find an expression for μ K in terms of your experimental parameters. 3. Run the experiment: Measure the kinetic friction force for six different loads on the block.
First run the block by itself, with no extra weights on it. Try both of the methods that you derived above, and decide which method is more experimentally workable. After the first trial, put weights on the block in the range 100 500 grams to provide extra load. Calculate F N, F K and their ratio μ K for each trial. Record all data and calculations in your lab notebook. Record your observations and conclusions about the results. 4. (Post-Lab) Analyze the results Plot F K versus F N on graph paper. Find the slope of the graph and write down its equation. This equation is your empirical force law for kinetic friction in this case. From your calculations, find the deviations and the average deviation for the coefficient of kinetic friction. Report your value for the coefficient in the form μ = μ average +/- δ, where δ is the average deviation. Experiment 2: Kinetic Friction and Surface Area Objective: How will the kinetic friction force change if the area of contact changes? Run the kinetic friction experiment with the narrow edge of the block in contact with the plank. Use the same set of loads as in experiment 1. Calculate the magnitude of the frictional forces and the coefficient of kinetic friction for each trial. Find the average value for the coefficient and compare your result here with your result for the wide face of the block. (Post-Lab): Find the deviations and average deviation in the results. Find the percent difference between your result in this case and your result using the wide face of the block. Draw a conclusion about the effect of surface area on the frictional force.
Experiment 3: Static Friction on Inclined Plane. What force holds the wood block in place? Objectives: What is the strength of the static friction force? How does the coefficient change with changing load? How do the coefficients of maximum static friction for various materials compare? Set up the system illustrated in the photograph above. The plank is supported by a horizontal rod at one end. (There is a hole in the side of the plank to support the rod.) The horizontal rod is supported by a right angle clamp which is clamped to the upright rod. Starting at a low angle of inclination, loosen the clamp and slowly increase the angle of the plank by raising the horizontal rod. When the block slides, tighten the clamp on the upright rod and measure the angle. The angle just before the block begins to slide is called the maximum angle of repose. Note that the block does not slide at first: it remains at equilibrium until the maximum angle is reached, even though the force of gravity pulling it down the plane increases as the angle increases. We conclude from this that the force of static friction is variable, taking on whatever value necessary to resist an opposing force up to some maximum value. The coefficient of static friction μ S is defined as the ratio of the static friction force to the normal force at this maximum value. We now want to develop a method for determining this value, and the coefficient, for this setup.
1. Analyze the forces on the block on the inclined plank when it is in equilibrium. Draw a Free Body Diagram for the forces on the block when it is at rest. Use a coordinate system in which the positive x-axis points down the plank. Break all forces into components parallel with the x- and y-axes: θ Referring to your FBD, write down expressions for the force of static friction and for the normal force on the block. These expressions give you a way to measure each force when the block is in equilibrium. Find an expression for the coefficient of static friction by dividing the expression for the frictional force by the expression for the normal force. This gives you a way to measure the coefficient. 2. Measure the coefficient of static friction for the wood block on the wood plank. Find the limiting angle of repose of the block in at least 5 trials. For each trial, calculate the force of friction, the normal force and the coefficient. Tabulate these results and average them. How does μ S compare with μ K? 3. Determine whether the coefficient of static friction varies with load. Use the brass weights in your weight set to find the coefficient of static friction for brass on wood. (We cannot add mass to the wood block for this can you guess why?) Use the 50-, 100-, 200- and 500-gram brass pieces for this.
Tabulate your values for the load and for the calculated coefficient. Draw a conclusion from the results. Are the results consistent with the expression you derived? 4. Find the coefficient of static friction for several other materials. You already have values for wood on wood and brass on wood. Now try some or all of these: o Aluminum o Lead o Stone o Rubber o Glass or other materials. Find the maximum angle of repose for these materials and calculate their coefficients using the expression you derived above. 5. Post-Lab Analysis Look up reference values for the coefficients of wood on wood and metal on wood. (The wood blocks and many of the wood planks are maple; some wood planks are pine.) How do your values compare to these?