Question

To measure the coefficient of kinetic friction by sliding a block down an inclined plane the block must be in equilibrium.

Answer 1

Answer:

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:

        $F_{gp} = m*g* sin \theta (1)$

       (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:

       $F_{f} = \mu_{k} * N (2)$

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

       $N = m*g* cos \theta (3)$

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

        $m*g* sin \theta = \mu_{k} * m*g* cos \theta$

• 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:

        $\mu_{k} = tg \theta$