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In order to determine the coefficients of friction between rubber and various surfaces, a student uses a rubber eraser and an incline. In one experiment, the eraser begins to slip down the incline when the angle of inclination is 36.7� and then moves down the incline with constant speed when the angle is reduced to 30.1�. From these data, determine the coefficients of static and kinetic friction for this experiment.

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lcmendozaf

Answer:

μs = 0.75

μk = 0.58

Explanation:

From a force diagram:

[tex]m*g*sin \theta - Ff=m*a[/tex]     (1)

[tex]N-m*g*cos \theta = 0[/tex]         (2)

When it starts slipping, friction force is the maximum and acceleration is 0. Replacing these conditions on (1):

[tex]m*g*sin \theta - \mu*m*g*cos \theta=0[/tex]   Solving for μs:

[tex]\mu=tan \theta[/tex]

μs = tan 36.7° = 0.75

When it moves at constant speed, friction force is kinetic friction and acceleration is 0. With these conditions the coefficient is:

μk = tan 30.1° = 0.58

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