A child weighing 140 N sits at rest at the top of a playground slide that makes

Question

A child weighing 140 N sits at rest at the top of a playground slide that makes an angle of 31° with the horizontal. The child keeps from sliding by holding onto the sides of the slide. After letting go of the sides, the child has a constant acceleration of 1.1 m/s2 (down the slide, of course). (a) What is the coefficient of kinetic friction between the child and the slide? What (b) minimum and (c) maximum values for the coefficient of static friction between the child and the slide are consistent with the information given here? (a) Number (b) Number (c) Number Units (0) Number units Units

Explanation / Answer

Given,

mass of the object, m = W/g

   m = 140/9.8 = 14.29 kg

acceleration, a = 1.1 m/s^2

angle ? = 31 degree

(a) Applying the Newton's 2nd law of motion,

   mgsin? - ?mscos? = ma

?k = (gsin 31° -a)/gcos 31°

       = 0.47

(b) the static ?s = tan31° = 0.60

the maximum,?s = 0.60

the minimum   ?s > 0.47

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