Question

A child weighing 150 N sits at rest at the top of a playground slide that makes an angle of
32o 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 1.0 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 maximum values for the coefficient of static friction between
the child and the slide are consistent with the information given here?

Answer 1

I'm stuck on (b)

Answer 2

One of the values of static friction , is when the Resistive and Driving forces, R and Fd, respectively are the same.
\[F _{d}=mgsin \alpha=150\sin32=79.49N \]
Normal contact force(N) is found by the difference in forces vertically:
\[150-150\cos(90-32)=70.51\
The resistive force is found by \[muN\], where mu is the coefficient of friction.
When the body is stationary, both Driving and Resistive forces are equal .[muR=Fd rightarrowmu=Fd/R=79.49/70.51=1.127\]N\]