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: The mysterious sliding stones. Along the remote Racetrack Playa in Death Valley, California, stones sometimes gouge out prominent trails in the desert floor, as if they had been migrating. For years curiosity mounted about why the stones moved. One explanation was that strong winds during the occasional rainstorms would drag the rough stones over ground softened by rain. When the desert dried out, the trails behind the stones were hard-baked in place. According to measurements, the coefficient of kinetic friction between the stones and the wet playa ground is about 0.640. What horizontal force is needed on a stone of typical mass 11 kg to maintain the stone's motion once a gust has started it moving?

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cjrodriguez89

Answer:

F= 69 N

Explanation:

  • Once in movement, the minimum force applied horizontally to maintain the stone's motion, must be equal in magnitude, to the kinetic friction force.
  • This friction force, can be expressed as follows:

        [tex]F_{f} = \mu_{k} * F_{n} (1)[/tex]

  • where μk = coefficient of dynamic friction = 0.640, and Fₙ = Normal Force.
  • The normal force, is always perpendicular to the surface on which the object is placed, and always aims upward.
  • As the friction force, the normal force can adopt any value needed to prevent the object to accelerate in the vertical direction, going through the surface under the influence of gravity.
  • In this case, if the floor is level, we have the following equation:

        [tex]F_{n} = m*g[/tex]

  • Replacing in (1) , we have:

       [tex]F_{f} = \mu_{k} * F_{n} = 0.640 * 11 kg* 9.8 m/s2 = 69 N\\ \\ F_{f} = F_{min}[/tex]

  • ⇒    Fmin = 69 N

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