Discussion and Review

Whenever a body slides along another body a resisting force is called into play that is known as friction. This is a very important force and serves many useful purposes. A person could not walk without friction, nor could a car propel itself along a highway without the friction between the tires and the road surface. On the other hand, friction is very wasteful. It reduces the efficiency of machines because work must be done to overcome it and this energy is wasted as heat. The purpose of this experiment is to study the laws of friction and to determine the coefficient of friction between two surfaces. THEORY

Friction is the resisting force encountered when one surface slides over another. This force acts along the tangent to the surfaces in contact. The force necessary to overcome friction depends on the nature of the materials in contact, on their roughness or smoothness, and on the normal force but not on the area of contact or on the speed of the motion. We find experimentally that the force of friction is directly proportional to the “normal force.” When an object is sitting on a horizontal surface the normal force is just the weight of the object. However, if the object is on an incline then it is not equal to the weight but is calculated by N= mg cos θ. The constant of proportionality is called the coefficient of friction, µ. When the contacting surfaces are actually sliding one over the other the force of friction is given by

Equation 1:

Ffr = µk FN

where Ffr is the force of friction and is directed parallel to the surfaces and opposite to the direction of motion. FN is the normal force and µk is the coefficient of kinetic friction. The subscript k stands for kinetic, meaning that µk is the coefficient that applies when the surfaces are moving one with respect to the other. µk is therefore more precisely called the coefficient of kinetic or sliding friction. Note carefully that Ffris always directed opposite to the direction of motion. This means that if you reverse the direction of sliding, the frictional force reverses too. In short, friction is always against you. Friction is called a “non-conservative” force because energy must be used to overcome it no matter which way you go. This is in contrast to what is called a “conservative” force such as gravity, which is against you on the way up but with you on the way down.

Thus, the energy expended in lifting an object may be regained when the object descends. Yet, the energy used to overcome friction is dissipated, which means it is lost or made unavailable as heat. As you will see in your later study of physics the distinction between conservative and non-conservative forces is a very important one that is fundamental to our concepts of heat and energy. A method of checking the proportionality of Ffr, and FNand of determining the proportionality constant µk is to have one of the surfaces in the form of a plane placed horizontally with a pulley fastened at one end. The other surface is the bottom face of a block that rests on the plane and to which is attached a weighted cord that passes over the pulley. The weights are varied until the block moves at constant speed after having been started with a slight push. Since there is no acceleration, the net force on the block is zero, which means that the frictional force is equal to the tension in the cord.

This tension, in turn, is equal to the total weight attached to the cord’s end. The normal force between the two surfaces is equal to the weight of the block and can be increased by placing weights on top of the block. Thus, corresponding values of Ffr,and FN can be found, and plotting them will show whether Ffrand FN are indeed proportional. The slope of this graph gives µk. When a body lies at rest on a surface and an attempt is made to push it, the pushing force is opposed by a frictional force. As long as the pushing force is not strong enough to start the body moving, the body remains in equilibrium.

This means that the frictional force automatically adjusts itself to be equal to the pushing force and thus to just be enough to balance it. However, there is a threshold value of the pushing force beyond which larger values will cause the body to break away and slide. We conclude that in the static case where a body is at rest the frictional force automatically adjusts itself to keep the body at rest up to a certain maximum. But if static equilibrium demands a frictional force larger than this maximum, static equilibrium conditions will cease to exist because this force is not available and the body will start to move. This situation may be expressed in equation form as:

Equation 2:

Ffr ≤ µsFN or Ffr max = µsFN

Where Ffris the frictional force in the static case, Ffr max is the maximum value this force can assume and µsis the coefficient of static friction. We find that µsis slightly larger than µk. This means that a somewhat larger force is needed to break a body away and start it sliding than is needed to keep it sliding at constant speed once it is in motion. This is why a slight push is necessary to get the block started for the measurement of µk.

One way of investigating the case of static friction is to observe the so-called “limiting angle of repose.” This is defined as the maximum angle to which an inclined plane may be tipped before a block placed on the plane just starts to slide. The arrangement is illustrated in Figure 1 above. The block has weight W whose component Wcosθ (where θ is the plane angle) is perpendicular to the plane and is thus equal to the normal force, FN. The component Wsin θis parallel to the plane and constitutes the force urging the block to slide down the plane. It is opposed by the frictional force Ffr, As long as the block remains at rest, Ffr must be equal to W sin θ. If the plane is tipped up until at some value θmax the block just starts to slide, we have:

Equation 3:

But:

Hence:

Or:

Thus, if the plane is gradually tipped up until the block just breaks away and the plane angle is then measured, the coefficient of static friction is equal to the tangent of this angle, which is called the limiting angle of repose. It is interesting to note that W cancelled out in the derivation of Equation 3 so that the weight of the block doesn’t matter.

PROCEDURE

This experiment requires you to record measurements in Newtons. Remember that in SI units the unit of force is called the Newton (N). One Newton is the force required to impart an acceleration of 1m/s2 to a mass of 1 kg. Thus 1 N = 1 kg.m/s2. You can convert any kg-mass to Newtons by multiplying the kg-weight by 9.8 m/s2, i.e., 100 g = 0.1 kg = 0.1 x 9.8 = .98 N. 1.

Determining force of kinetic or sliding friction and static friction a. The wooden blocks provided in the LabPaq are too light to give good readings so you need to put some weight on them, such as a full soft drink can. Weigh the plain wood block and the object used on top of the block. Record the combined weight in grams and Newtons.

b. Place the ramp board you provided horizontally on a table. If necessary tape it down at the ends with masking tape to keep if from sliding.

c. Begin the experiment by setting the block and its weight on the board with its largest surface in contact with the surface of the board. Connect the block’s hook to the 500-g spring scale. d. Using the spring scale, slowly pull the block lengthwise along the horizontal board. When the block is moving with constant speed, note the force indicated on the scale and record. This is the approximate kinetic or sliding frictional force. Repeat two more times.

e. While carefully watching the spring scale, start the block from rest. When the block just starts to move, note the force indicated on the scale and record. You should notice that this requires more force. This force is approximately equal to the static frictional force. Repeat two more times.

Determining coefficient of static friction using an inclined surface

a. Place the plain block with its largest surface in contact on the board while the board is lying flat.

b. Slowly raise one end of the board until the block just breaks away and starts to slide down. Be very careful to move

the plane slowly and smoothly so as to get a precise value of the angle with

the horizontal at which the block just breaks away. This is the limiting angle of repose θ max. Measure it with a protractor (see photo that follows for an alternate way of measuring the angle) and record the result. You may also want to measure the base and the height of the triangle formed by the board, the support, and the floor or table. The height divided by the length of the base equals the coefficient of static friction.

Remember:

c. Perform two more trials. These trials should be independent. This means that in each case the plane should be

returned to the horizontal, the block placed on it, and the plane carefully moved up until the limiting angle of repose is reached.

DATA TABLE 6

Height

Base Length

θ max

µs

Trial 1

Trial 2

Trial 3

Average

Calculations

1. Using the mass of the block and the average force of kinetic friction from Data Table 1, calculate the coefficient of kinetic friction from Equation 1:

2. Using the mass of the block and the average force of kinetic friction from Data Table 2, calculate the coefficient of kinetic friction for the wood

block sliding on its side. Record your result and see how it compares with the value of µkobtained from Data Table 1.

3. From the data in Data Table 3, 4 & 5 compute the coefficient of static friction, µsfor, the glass surface on wood, the sandpapered surface on wood, and wood on carpet, etc from each of your three trials. Calculate an average value of µs.Record your results in your own data sheets.

4. From the data obtained in Data Table 6 calculate µsfor wood on wood from each of your three trials.

5. Calculate an average value of µs. Record your result on the data sheet.

Questions

A. How does the coefficient of static friction compare with the coefficient of kinetic friction for the same surfaces and areas?

B. Why is it important to reduce friction during the operation of machinery? C. How does grease or oil affect the coefficient of friction?