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Old Apr 10th 2012, 09:15 PM   #1
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Exclamation The Slope of a Normal Force vs Applied Force Graph

1. The problem statement, all variables and given/known data
An experiment was conducted where a slider with different mass combination is placed on a board. A newton spring scale is attached to the slider and is pulled horizontally and parallel to the board such that the slider moves at a constant velocity. The applied force required to move the slider at a constant velocity is recorded and the total mass is also recorded. The purpose of this experiment is to determine the value of the coefficient of kinetic friction between the slider and the board by graphing the relation between normal force and applied force.

With total mass, I can determine the force of gravity since Fg = ma. Then, because the object is not moving vertically, Fg = Fn in magnitude.

Now to find the kinetic friction, one get simply used the magnitude of the applied forces. This is due to the fact that the slider was assumed to be moving at a constant velocity, Newton's First Law, net force equals zero.

The relation between normal force and applied force can then be graphed. (x-axis is the normal force and y-axis is the applied force)
Now here is the problem:

2. Relevant equations
To determine the coefficient of kinetic friction, one would need to calculate the slope of the graph. The question arise at: Does the line start at point (0,0)? or just a line of best fit among the 3 data points which I had conducted (in which case the line would not have an x-value (normal force) of 0 when the y-value (applied force) is 0?)

3. The attempt at a solution
Now my reason was that the line must not touch the point (0,0), the reason being one, we do not have a data point at (0,0) and two, when the applied force equals to 0, the normal force will not equal to 0, as the forces are perpendicular and serves no purpose in cancelling each other out. Also, because gravity always attract, as long as the object remains at rest on a surface, a normal force would had counter the force of gravity so that Fnety equals 0 (Newton's First Law). Moreover, since the mass of the object cannot be zero, the normal force must have a value greater than 0 (because Fn = Fg = mg) even when the object is at rest horizontally.

However, my classmates argued that it would not matter at all as the proportional constant (the coefficient of kinetic friction) would still be able to govern the values between force of kinetic friction and normal force.

This leads me thinking to another problem, since μk = Fk/Fn, if both of your kinetic friction and normal force equals to 0, it would lead to an undefined value for μk (because dividing by 0), which would create an asymptote on the graph. Such should not be possible.

Regardless, I am not sure whether my reasoning is correct or not, please kindly contribute your opinion should you have any.

Your contribution is sincerely appreciated. Thank you.
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Old Apr 11th 2012, 05:47 AM   #2
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Well, I believe that the normal force is always equal to mg when the slider is at rest. It is the coefficient of friction which changes.

Since it's more difficult to visualise the coefficient of kinetic friction at work, I'll use the coefficient of static friction instead.

Say you have a big heavy drum. Applying a force greater than 1000 N moves it. If you apply 1 N, nothing happens, or if it was 500 N, nothing happens. Even with 1000 N, nothing would happen.

The normal force is still there... but then something is changing!
[I'll use R as the normal force]

F = μR

F = 1000
R = mg [constant]

So, μ is taking in values so that ultimately, the equation holds.

μ will vary from 0 to a maximum value, which is attained when constant velocity or the magnitude of velocity increases.

Hence, applying no force on the slider would cause μ to be 0. As Fk increases, μ will increase until a point where it becomes constant.
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