Respuesta :
Complete Question:
A child is playing in a park on a rotating cylinder of radius, r = 3.00 m , is set in rotation at an angular speed of w = 5.00 rad/s. The base of the cylinder is slowly moved away, leaving the child suspended against the wall in a vertical position. What is the minimum coefficient of friction between the child's clothing and wall needed to prevent it from falling
Answer:
minimum coefficient of friction between the child's clothing and wall needed to prevent it from falling, [tex]\mu = 0.131[/tex]
Explanation:
Applying the Newton's law:
[tex]\mu N = mg[/tex]...............(1)
Where N = Normal reaction.
and [tex]\mu[/tex] = coefficient of friction
Since the cylinder is a rotating one, the normal reaction will be calculated using the formula [tex]N = \frac{mv^{2} }{r}[/tex].................(2)
Substituting (2) into (1)
[tex]\mu \frac{ mv^{2} }{r} = mg[/tex].............(3)
v = wr..........(4)
Substitute (4) into (3)
[tex]\mu \frac{ m\omega^{2} *r^{2} }{r} = mg\\\mu \omega^{2} *r = g\\\mu = \frac{g}{\omega^{2} r }[/tex]
Substituting, w, g, and r into the equation above
Angular speed, [tex]w = 5 rad/s[/tex]
Radius, r = 3 m
g = 9.8 m/s²
[tex]\mu = \frac{9.8}{5^{2} *3 }[/tex]
[tex]\mu = 9.8/75\\\mu = 0.131[/tex]
