Frictional Forces

Pre-Lab Questions and Exercises:

1. Identify at least 4 factors that could affect friction and will be investigated in this lab.
2. Why is the normal force used in Equation 1 instead of the weight of the object?
3. When measuring the force of kinetic friction, why is it important that the block be pulled at constant velocity?
4. Show the derivation of Equation 3 by using a free-body diagram and applying Newton’s second law.

Introduction

Friction is the resistance to the relative motion of materials in contact with each other. While we often think of friction in a negative sense, and many physics problems ignore friction or assume that it is negligible, the fact is that without friction, we would have great difficulty getting anywhere! Certainly anyone who has fallen on a slippery surface or had difficulty getting up an ice-covered hill in a car can attest to the importance of friction.

Friction between surfaces results from microscopic irregularities, and ultimately involves electrical interactions on the atomic and molecular level. While the details of friction are quite complex (the study of friction is formally called tribology), the macroscopic properties can be examined and explained in rather simple terms.

When an object slides over a surface, the frictional force opposing the motion is called kinetic friction. To a good approximation, this kinetic frictional force f_k is proportional to the normal force N of the surface pushing against the object:

Equation 1

where m_k is the coefficient of kinetic friction between the two surfaces.

For an object that is not moving, the force of static friction f_s is equal in magnitude to the applied force and is related to the normal force N, by equation two:

Equation 2

where the equal sign is only used when the object is on the verge of moving; otherwise the frictional force is less than this maximum static frictional force. If there is no applied force, then there is no frictional force.

The coefficient of static friction can also be found from the angle at which an object begins to slide down an incline (maximum angle of repose), q:

Equation 3

Likewise, m_k can be found from the angle at which an object slides down an incline at constant velocity.

Below is a table of coefficients of friction between various common materials:

Note: All values are approximate

m_s m_k

Steel on steel 0.74 0.57

Aluminum on steel 0.61 0.47

Copper on steel 0.53 0.36

Wood on wood 0.25-0.5 0.2

Glass on glass 0.94 0.4

Rubber on concrete (dry) 0.9 0.8

Rubber on concrete (wet) 0.3 0.25

Waxed wood on wet snow 0.14 0.1

Waxed wood on dry snow ----- 0.04

Steel on ice 0.10 0.06

Metal on metal (lubricated) 0.15 0.06

Ice on ice 0.1 0.03

Teflon on Teflon 0.04 0.04

Synovial joints in humans 0.01 0.003

Reference: Table 4.2 in College Physics by Serway and Faughn, 6^th ed.

Procedure:

Part 1 – Level Surface:

Place the block on the aluminum track. Attach a spring scale to the block and pull slowly until the block moves with constant velocity. Note the maximum force that is required to start the block moving (f_s,max). Record also the force required to keep the block moving at constant velocity (f_k). Compare these values – which is greater? Use the weight of the block to calculate the coefficients of static and kinetic friction.

Attach the LabPro interface and force probe to your computer. Launch Logger Pro and use the spring scale to calibrate (Under the Experiments menu, click Calibrate). Click the collect button and use the force probe to drag the block along the track, periodically stopping and starting again. Sketch the graph. [Note that you can use the autoscale, examine, and statistics buttons (shown below) to get information from your graph.] Do the values of f_s,max and f_k agree with your previous values? Discuss how you determined these values from the graph.

Using the force probe, measure the kinetic frictional force at two different constant velocities. Is there any significant difference in the force of friction at low versus high speed? How can you tell from the graph if you are moving at a constant velocity?

Again using the force probe, examine the effect of surface area. While keeping other parameters constant, measure the force of kinetic friction for the two wooden surfaces. To do this, place the block on the small wooden surface, evenly load it with masses, and measure the kinetic frictional force. Repeat this with the block on the large wooden surface loaded with the same masses. How does the surface area affect the frictional force?

Evenly distribute masses on top of the block to approximately double the normal force (~200g) and use the force probe to measure the kinetic frictional force. Continue adding masses and taking measurements to obtain at least five sets of forces. Record these results in a data table. Plot this data on a graph of frictional force versus normal force. Are these quantities directly proportional as expected? What is the y-intercept? From the graph, determine the coefficient of friction. Repeat this procedure for at least three different combinations of surfaces. (ie. Wood/Al, Rubber/Al, Cork/Al, Wood/Rubber, Rubber/Rubber, or Cork/Rubber) Be sure to record which combination of surfaces corresponds to each set of data.

Part 2 – Inclined Plane:

For each of the surfaces examined in part 1, find the coefficients of static and kinetic friction from angle of repose (see Equation 3). To do this you will slowly raise one end of the track until the block begins to slide. Do these values agree with the values determined in part one?

Discussion:

Based on the empirical evidence that you gathered in this lab, what discoveries did you make about frictional forces? Did you find that surface area or relative speed had any significant effect on the frictional force? Is the coefficient of static friction always greater than kinetic friction? Is the difference the same for different surfaces? What about the relative difference? Why should m not be reported to more than 2 significant figures? Discuss the sources of uncertainty for parts one and two. What other investigations could you suggest for this lab? (ex. How could you use a photogate to determine the force of friction?)

Additional questions for discussion:

1. If friction does not depend on surface area, why are wide tires used on race cars?
2. What is the maximum acceleration of a car with rubber tires?
3. When driving a car, why is it recommended that you turn into a skid?