Question

find the coefficient of kinetic friction between the child and the slide if the slide is inclined at an angle of 28° below the horizontal

Answer 1

Given:

The acceleration of the child, a=1.26 m/s²

The angle of inclination, θ=28°

To find:

The coefficient of kinetic friction between the child and the slide.

Step-by-step explanation:

The net force acting on the child when it is sliding down the slide is given by,

`\begin{gathered} ma=mg\sin\theta-f \\ =mg\sin\theta-N\mu \\ =mg\sin\theta-mg\cos\theta\text{ }*\mu \end{gathered}`

Where f is the frictional force, N is the normal force acting on the child, g is the acceleration due to gravity, and μ is the coefficient of kinetic friction.

On simplifying the above equation,

`\begin{gathered} a=g\sin\theta-g\mu\cos\theta \\ \implies g\mu\cos\theta=g\sin\theta-a \\ \implies\mu=(g\sin\theta-a)/(g\cos\theta) \end{gathered}`

On substituting the known values,

`\begin{gathered} \mu=(9.8\sin28\degree-1.26)/(g\cos28\degree) \\ =0.386 \end{gathered}`

Final answer:

The coefficient of kinetic friction between the child and the slide is 0.386