Kinetic & Static Friction When two objects touch, they exert a force on each other through surface contact. We call the component of this force that is perpendicular to the surface the normal force. We call the component of this force that is parallel to the surface a friction force. Frictional forces oppose any sliding between 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 overall. The sum 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, FK, 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, FS, 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 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: μK for the coefficient of kinetic friction and μS 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 slides at constant speed.

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. Find an expression for the frictional force on the block, FK in terms of the masses of the block and the hanging mass. •

You will use the expression to determine FK experimentally. Since there are two masses in the experiment, start by drawing a free-body diagram for the block as it slides, and for the hanging mass. Use coordinates like this: +y

+y Mass 2

Block: Mass 1 +x +x

Note that the x-axis points along the string.

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For each mass, write out ΣFx = max (Newton’s 2nd Law of Motion) for acceleration in the x-direction. Be sure to distinguish between Mass 1 and Mass 2.

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Using the fact the tension in the string is the same for each mass, and that they will have the same acceleration as the block slides, combine the two expressions and solve for FK.

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You could use this result if you measured the acceleration of the system. It will be easier, however, to arrange for an acceleration of zero (the block moves at constant speed). Modify your expression above for the case of ax = 0. You can use the result to measure the frictional force on the block.

2. Now find an expression for the coefficient of kinetic friction, μK. •

Looking at your FBD, decide how you can determine the normal force, FN, between the block and the plank.

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Apply the definition of the coefficient of kinetic friction (μK = FK/FN) to find an expression for μK in terms of the mass of the block (and any mass set on top of the block) and the hanging mass.

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. By trial and error, find the hanging mass such that the system moves at constant speed. You must set the block in motion with a small push, since otherwise static friction will hold it in place. (If you were to find the hanging mass necessary to start the block moving, you would be measuring static friction.)

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After the first trial, put weights on the block in the range 100 – 500 grams to provide extra load.

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Calculate FN, FK and their ratio μK for each trial. Record all data and calculations in your lab notebook.

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Record your observations and conclusions about the results.

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.

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?

First: 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 of inclination. The angle just before the block begins to slide is called the maximum angle of repose. Note that the block does not slide at low angles: 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 μS 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 the weight of the block into components parallel with the x- and y-axes:

θ

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Referring to your FBD, write down expressions for the force of static friction and for the normal force on the block in terms of the inclination angle. 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 6 trials: Start with the plank horizontal and slowly elevate the plank until the block slides. Record your results for the limiting angle of repose and find the average. Calculate the force of static friction at this limiting angle, and calculate the coefficient of static friction for wood on wood. How does μS compare with μK?

3. Find the coefficient of static friction for several other materials. •

You already have values for wood on wood. Now try some or all of these: o o o o o o

Aluminum Brass Lead Stone Rubber Glass

or other materials. Find the maximum angle of repose for these materials and calculate their coefficients using the expression you derived above.

Post-Lab Analysis Kinetic friction: Wide face of Block •

Plot FK versus FN 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.

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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 = μaverage +/- δ, where δ is the average deviation.

Kinetic Friction: Effect of Surface Area •

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. Suggest an explanation for your results.

Static Friction on Incline •

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?

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Find the uncertainty in your value for the coefficient of static friction, wood on wood. To do this, find the average deviation for the maximum angle of repose in the several trials. Use the average deviation as the uncertainty in the maximum angle. Then take the derivative of your expression for the coefficient to find the rate of change of the coefficient, and from this the uncertainty: Δμ= dμ/dθ Δθ Note: You must use radian measure for the angles.