## Essential University Physics: Volume 1 (3rd Edition)

We need to know the two forces causing the child to go downward. We know that there is the force of gravity pulling the child down the hill: this equals $mgsin\theta$. However, there is also a frictional force acting directly up the hill: this is given by $=F_n\mu$. The normal force is equal to the cosine of theta times the force of gravity, so we find: $F_f=\mu mgcos\theta$. The child is going at a constant speed, so we know that the two forces are equal. Thus: $\mu mgcos\theta=mgsin\theta\\ \mu=\frac{sin8.5}{cos8.5}=.149$