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An experiment designed to measure the coefficient of kinetic friction between the bottom surface of a wooden box, lined with felt, and a glass plate placed on an inclined plane. the procedure for conducting the experiment, including determining the angle of elevation of the plane and calculating the masses involved. The data obtained from the experiment is used to plot a graph and perform a linear regression to determine the coefficient of kinetic friction.
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When two surfaces in contact move relative to one another in a direction tangent to the surfaces, each surface exerts a shearing force on the other. This force referred to as kinetic friction, although complicated in origin, satisfies a simple mathematical relationship, fk = μkN , (1)
where fk, the kinetic friction force, is exerted tangent to the surface and opposite to its direction of motion. Here, N is the force that one surface exerts normal to the other surface, and μk, the coefficient of kinetic friction, depends only on the intrinsic properties of the two surfaces in contact. [1] The purpose of this experiment is to determine the coefficient of kinetic friction be- tween the bottom surface of a wooden box, lined with felt, and a glass plate positioned on an inclined plane, as shown in Figure 1. Given the block positioned on the plane
Figure 1: Box and Inclined Plane
inclined at angle θ, let M be the amount of mass suspended from the string, such that when the box, initially at rest, is nudged up the incline, it moves with constant velocity. Correspondingly, let m be the amount of mass attached to the string, such that when
the box is nudged down the incline, it moves with constant velocity down the incline. It can be shown that M − m M + m
= μk cot(θ). (2)
Insert a 500 gram mass and two 100 gram masses in the box, as shown in Fig. 2.
In performing the experiment you are instructed to nudge the box so that it moves with constant velocity. In order to obtain acceptable experimental results, this proce- dure should be performed in a consistent way. The following is a suggestive, but not necessarily prescriptive, way of satisfying this condition:
(^1) When adding mass to the mass holder, do so in increments of 20 grams or larger throughout the experi- ment.
and the standard error of the intercept δB is
δB = σy
1 − r^2 N − 2
x¯^2 σ x^2
where r is the estimated correlation coefficient between the yi and xi, σy and σx are the estimated standard deviations of the yi and xi, and x¯ is the estimated average of the xi.^2 The quantities x¯, σx, and σy can straightforwardly be calculated using function keys on a scientific calculator or defined functions in Excel. If, in the regression equation, Eq. 3, the quantity B, the y-intercept, is required to be zero, i.e. the regression equation is now yi = M xi + i , (6)
then the degrees of freedom in the random errors are N − 1 rather than N − 2 so that
δM =
1 − r^2 N − 1
σy σx
To reflect the statistical uncertainty in a quantity Q, where Q is either the slope M or y-intercept B, the quantity Q is typically reported as
Qest ± δQ , (8)
which can be understood informally to mean that, assuming the experimental results are consistent with theory, then the value of Q, predicted by theory, is likely to lie within the limits defined by Equation 8.
[1] Wikipedia. Friction. http://en.wikipedia.org/wiki/Friction,
(^2) Note: in Equation 5 σx and σy are unbiased estimates.
Case θ◦^ M (gms) m (gms) cot(θ) MM^ −+mm 1 2 3 4 5
Table 1: Data and Computations
Table 2: The experimental value of the coefficient of kinetic friction, μk