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.
Explanation:
The net force acting on the child when it is sliding down the slide is given by,
[tex]\begin{gathered} ma=mg\sin\theta-f \\ =mg\sin\theta-N\mu \\ =mg\sin\theta-mg\cos\theta\text{ }\times\mu \end{gathered}[/tex]
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,
[tex]\begin{gathered} a=g\sin\theta-g\mu\cos\theta \\ \implies g\mu\cos\theta=g\sin\theta-a \\ \implies\mu=\frac{g\sin\theta-a}{g\cos\theta} \end{gathered}[/tex]
On substituting the known values,
[tex]\begin{gathered} \mu=\frac{9.8\sin28\degree-1.26}{g\cos28\degree} \\ =0.386 \end{gathered}[/tex]
Final answer:
The coefficient of kinetic friction between the child and the slide is 0.386
