# The Slope of a Normal Force vs Applied Force Graph

## Homework Statement

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:

## Homework 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?)

## 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.

Last edited:

ehild
Homework Helper
The relation between normal force and applied force should be of form F(applied)=μFn, so the straight line fitted to the data points should go through the origin. But the measured data have some errors. You have to be sure that the force meter is calibrated properly, reading zero force when unloaded. The systematic error would cause the plot shift along the y axis otherwise. The same holds for the scales you measured mass.
If you see that the data points fit well on a straight line which avoids the origin you can suspect systematic error of measurement and determine μ from the slope of that straight line.

ehild

The relation between normal force and applied force should be of form F(applied)=μFn, so the straight line fitted to the data points should go through the origin. But the measured data have some errors. You have to be sure that the force meter is calibrated properly, reading zero force when unloaded. The systematic error would cause the plot shift along the y axis otherwise. The same holds for the scales you measured mass.
If you see that the data points fit well on a straight line which avoids the origin you can suspect systematic error of measurement and determine μ from the slope of that straight line.

ehild

Thank you for replying by ehild.

I agree that there does exist some errors in conducting the experiment, I had mentioned them in my lab report. But since there exist these errors, would I still draw the straight line passing through the origin? In the lab outline, it asked us to calculate the slope of the graph and did not specify on any details regarding to where the line was a slope of the data points or a line of best fit.

If I do draw the slope passing through the origin, it is true that I can use (0,0) as the coordinate to calculate my slope correct?

ehild
Homework Helper
In principle the slope belongs to the best-fit straight line which might not go through the origin.
When calculating the slope, do not use any measurement point. Choose points of the line near the first and last measured points. See picture.

ehild

#### Attachments

• fitslope.JPG
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It turns out my data points were very close to the line of best-fit that passes through the origin, so problem solved.

Thank you very much ehild!

ehild
Homework Helper
It turns out my data points were very close to the line of best-fit that passes through the origin, so problem solved.

Thank you very much ehild!

It was a good experiment then. You are welcome ehild