Question

A playground slide is in the form of an arc of a circle with a maximum height of 3.0 m, with a radius of 8.5 m, and with the ground tangent to the circle. Dr. Ritchey’s 12 kg daughter starts from rest at the top of the slide and has a speed of 4.5 m/s at the bottom. a. What is the length of the slide? b. What average frictional force acts on the child over this distance?

Answer 1

Answer:

a) $s \approx 6.676\,m$

Explanation:

a) Let assume that the ground is not inclined, since the bottom of the playground slide is tangent to ground. Then, the length of given by the definition of a circular arc:

$s = \frac{\pi}{4}\cdot R$

$s=\frac{\pi}{4}\cdot (8.5\,m)$

$s \approx 6.676\,m$

The bottom of the slide has a height of zero. The physical phenomenon around Dr. Ritchey's daughter is modelled after Principle of Energy Conservation. The child begins at rest:

$U_{g,A} = K_{B} + W_{fr}$

$m\cdot g \cdot h_{A} = \frac{1}{2}\cdot m \cdot v_{B}^{2} + f\cdot s$

The average frictional force is cleared within the expression:

$f = \frac{m\cdot (g\cdot h_{A}-\frac{1}{2}\cdot v_{B}^{2})}{s}$

$f = \frac{(12\,kg)\cdot [(9.807\,\frac{m}{s^{2}} )\cdot (3\,m)-\frac{1}{2}\cdot (4.5\,\frac{m}{s} )^{2} ]}{6.676\,m}$

$f = 34.684\,N$