To measure the coefficient of kinetic friction by sliding a block down an inclined plane the block must be in equilibrium.
What experimental condition must you try to accomplish that will assure you that the block is in equilibrium?

a. The block must slide down with a constant speed.
b. The block must slide down with a constant acceleration.
c. The block must be at rest.
d. The block must slide down with an acceleration of 9.8 m/s².

a)

Explanation:

A block sliding down an inclined plane, is subject to two external forces along the slide.One is the component of gravity (the weight) parallel to the incline.If the inclined plane makes an angle θ with the horizontal, this component (projection of the downward gravity along the incline, can be written as follows:

       

       (taking as positive the direction of the movement of the block)

The other force, is the friction force, that adopts any value needed to meet the Newton's 2nd Law.When θ is so large, than the block moves downward along the incline, the friction force can be expressed as follows:

       

The normal force, adopts the value needed to prevent any vertical movement through the surface of the incline:

       

In equilibrium, both forces, as defined in (1), (2) and (3) must be equal in magnitude, as follows:

       

As the block is moving, if the net force is 0, according to Newton's 2nd Law, the block must be moving at constant speed.In this condition, the friction coefficient is the kinetic one (μk), which can be calculated as follows:

       

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