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Dana manages to pull the sled up onto a hillside with a grade of 15 degrees. She stops and lets go of the rope when she realizes Dave forgot the hot chocolate! If the combined mass of Dave and the sled is 80kg, what is the minimum static friction force required to keep Dave from sliding back down the hill?

Respuesta :

Answer: The minimum Static force is [tex]F_{s}[/tex] = - 238.24 N.

Explanation: To determine the Static Friction Force, use:

[tex]F_{s}[/tex] = μ · [tex]F_{N}[/tex], where:

μ is coeficient of static force;

[tex]F_{N}[/tex] is the force perpendicular to the surface called normal force;

As the sled is up a hill with 15⁰ of grade, normal force is:

[tex]F_{N}[/tex] = m.g.cosθ

[tex]F_{N}[/tex] = 80*9.8*cos(15)

[tex]F_{N}[/tex] = - 595.6 N

The coeficient of static force is a known value: μ = 0.4, which is the coeficient of friction necessary to maintain the sled on the verge of sliding back the hill.

Calculating:

[tex]F_{s}[/tex] = μ · [tex]F_{N}[/tex]

[tex]F_{s}[/tex] = 0.4 . (- 595.6)

[tex]F_{s}[/tex] = - 238.24 N

The minimun necessary to keep Dave on the top of the hill is [tex]F_{s}[/tex] = - 238.24N. The negative sign indicates the sled is moving against the reference.

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