Answer:
a) [tex]s \approx 6.676\,m[/tex]
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:
[tex]s = \frac{\pi}{4}\cdot R[/tex]
[tex]s=\frac{\pi}{4}\cdot (8.5\,m)[/tex]
[tex]s \approx 6.676\,m[/tex]
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:
[tex]U_{g,A} = K_{B} + W_{fr}[/tex]
[tex]m\cdot g \cdot h_{A} = \frac{1}{2}\cdot m \cdot v_{B}^{2} + f\cdot s[/tex]
The average frictional force is cleared within the expression:
[tex]f = \frac{m\cdot (g\cdot h_{A}-\frac{1}{2}\cdot v_{B}^{2})}{s}[/tex]
[tex]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}[/tex]
[tex]f = 34.684\,N[/tex]
The average frictional force that acts on the child is 71.1 N
According to the question the radius of arc is r = 8.5 m, height h = 3m.
The length of the slide [tex]l =\frac{\pi}{4}\times8.5m= 6.67m[/tex]
Mass of the person m = 12kg. and the speed at the end point is v = 4.5 m/s.
From the law of conservation of energy, total meachanical energy at the starting point is equal to the total energy at bottom.
[tex]mgh+0=\frac{1}{2}mv^2+mg\times0+f.l[/tex]
where f.l is energy due to the work done by frictional force f.
[tex]12\times9.8\times3=0.5\times12\times(4.5)^2+f\times6.67\\\\6.67f=474.3\\\\f=71.1\;N[/tex]
The average frictional force acting on the person is 71.1 N.
Learn more about frictional force:
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