Experiment 5

###### The Coefficient of Kinetic Friction

Objective:

To determine the coefficient of kinetic friction between two selected surfaces by using a horizontal surface

Equipment:

A computer with internet connection, a calculator (The built-in calculator of the computer may be used.), paper, and pencil

Theory:

The Coefficient of friction is defined as the ratio of force of friction to the normal force, μ  = F / N .  Consider the following two Figures.  One is for static friction and the other for kinetic friction.  In this experiment, only the coefficient of kinetic friction will be measured.

 At constant velocity to the Right, F = F k. On the verge of motion to the Right, F = Fs μ k   = Fk / N .     Here, F = Fk  Fk = Force of kinetic friction,   μk  = coefficient of kinetic friction,   N  = Normal force or the force perpendicular to the contacting surfaces. μ s   = Fs / N .     Here, F = Fs  Fs = Force of static friction,   μs  = coefficient of static friction,   N  = Normal force or the force perpendicular to the contacting surfaces.

The force of friction acts against the direction of motion.   Note that  Fk < Fs  and consequently,  μk < μs .

If the externally applied force (F) is just equal to the force of static friction, Fs, then the object is on the verge of slipping, and the coefficient of friction involved is called the coefficient of static friction, μs.

If the externally applied force (F) is equal to the force of kinetic friction, Fk, then the object slides at constant velocity, and the coefficient of friction involved is called the coefficient of kinetic friction, μk.

In order to find the coefficient of kinetic friction between two surfaces, the horizontal surface method may be used as follows:

Horizontal Surface Method:

Referring to Fig. 1, it is clear that M has a tendency to move to the right because of F = mg.    F is resisted by the friction force Fk.  If m is great enough to slide M to the right at constant velocity, then F = Fk .    At a constant velocity of M to the right, we may write:

μ k= (Fk / N ) = (F / w) or,    μ k  = mg / Mg ,      or,  μ k  = m / M .   This means that the ratio m/M gives us a measure of μk. Procedure:

The link below may be used for the coefficient of friction, although it says Newton's 2nd Law.

Click on http://www.walter-fendt.de/ph14e/n2law.htm ; then,  click on the "start" button.

In this experiment, since the coefficient of kinetic friction is to be measured,  constant speed motion of  block M requires a zero acceleration.   In this applet, a zero acceleration means no motion; therefore, try to keep the acceleration nearly zero, under 0.010 m/s2 , to assure an almost constant velocity motion.  The coefficient of kinetic friction is the ratio F/w or mg/Mg , or simply m/M.   Based on the data you enter, if the ratio m/M is exactly equal to the selected μ, no motion will occur.  To cause motion, you need to slightly increase m, the hanging mass, by 0.1 gram, for example.  Make sure that the acceleration remains under 0.010 m/s2, close to zero enough for constant velocity motion.  You may need to practice for a while before doing the actual experiment.

Use the values of M, m, and μ in each row as given on the following Table:

In each run (row) try m such that the block slides at a nearly zero acceleration (under 0.01m/s2).

Make sure that the values of M and μ(Given) are correct for each case and row before running it.  For each row, calculate a μ (measured) and for each case, calculate the mean value of μ (measured) and record it under

 Case μ (Given) (Accepted) m(grams) M (grams) μ = m/Mμ (Measured) Mean value theMeasured μ %error 1 0.12 100. 200. 300 400 2 0.14 100 200 300 400 3 0.19 100 200 300 400 4 0.24 100 200 300 400

Graph: For Case 4 only, Graph (m versus M).  This is the same as graphing (F versus w), or the same as graphing (Fk versus N  ).  Since Fk is on the vertical axis and N on the horizontal axis, the slope of the line is  Fk / N  .

Data:

### Provide the necessary calculations in the Table.

Comparison of the results:

Use the following percent difference formula and calculate the percent difference in each case and record it in the Table. Conclusion:

State your conclusions of the experiment.

Discussion:

Provide a discussion if necessary.

Questions for Discussion:

1. Is the coefficient of kinetic friction the same for two surfaces regardless of the normal force?  Why?  Is your answer the same for the coefficient of static friction?
2. How does the value of the coefficient of static friction compare with the value of the coefficient of kinetic friction for the same surfaces?
3. How does the slope of the graph (in Case 4) compare with the coefficient of friction?