Experiment 5
Objective:
To determine the coefficient of kinetic friction between two surfaces by two different methods
Equipment:
A computer with internet connection, a calculator (The builtin calculator of the computer may be used.), paper, and pencil
Theory:
The coefficient of friction is defined as the ratio of friction force to the normal force, μ = F /N . Consider the following two cases: One measures the force of static friction and the other the force of kinetic friction.
At constant velocity to the Right, we must have F = F_{k }. This means that measuring the pulling force F is like measuring the force of static friction F_{k }.

On the verge of motion to the Right, F = F_{s}_{ }. This means that measuring the pulling force F is like measuring the force of static friction F_{s}_{ }.


μ _{k} = F_{k} /N . Here, F = F_{k}_{ }. F_{k} = Force of kinetic friction, μ_{k} = coefficient of kinetic friction, and N = normal to the contacting surfaces. 
μ _{s} = F_{s} /N . Here, F = F_{s } . F_{s} = Force of static friction, μ_{s} = coefficient of static friction, and N = normal to the contacting surfaces. 
The force of friction always acts against the direction of motion. Note that F_{k} < F_{s} and consequently, μ_{k} < μ_{s }.
If the externally applied force F just equals the force of static friction, F_{s}, then the object is on the verge of slipping, and the coefficient of friction involved is called the coefficient of static friction, μ_{s}.
If the externally applied force F just equals the force of kinetic friction, F_{k}, then the object slides at a constant velocity, and the coefficient of friction involved is called the coefficient of kinetic friction, μ_{k}_{ }.
In order to measure the coefficient of kinetic friction between two surfaces, the following two experimental procedures are to be followed:
Horizontal surface Method:
Referring to Fig. 3, it is clear that M moves to the right because of F = mg. The cord transmits force F to block M that pulls it. M_{ }is resisted by the friction force F_{k}_{ } . If F is much greater than F_{k }, motion definitely occurs and the system accelerates. We want motion to occur but at zero acceleration. It means at a constant velocity. For that to happen the pulling force F must exactly equal the friction force F_{k }. If you keep increasing m until F = mg equals F_{k }, then with some tapping on the surface motion will occur at constant velocity. At constant velocity of M to the right, we may write:
μ_{ k}= F_{k} /N = F /W or, μ_{ k} = mg /Mg , or,
μ_{ k} = m/M 
Procedure:
The following link may be used for measuring the coefficient of friction, although it says Newton's 2nd Law.
Click on http://www.walterfendt.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/s^{2} 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 m/M ratio 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/s^{2} 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 in Table 1.
In each run (row) try m such that the block slides at a nearly zero acceleration (under 0.01m/s^{2}).
Make sure that the values of M and μ (Given) are correct (in the applet) for each case (in each 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 the mean value column.
Table 1
Case

μ (Given) (Accepted) 
m (grams) 
M (grams) 
μ = m/M μ (Measured) 
Mean value the Measured 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 (F_{k} versus N ). Since F_{k} is on the vertical axis and N on the horizontal axis, the slope of the line is F_{k}/N .
Data:
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 conclusion(s) of the experiment.
Discussion:
Provide a discussion if necessary.
Questions:
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 two surfaces?
3) How does the slope of the graph (in Case 4) compare with the coefficient of friction?