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Sagot :
Hi there!
a)
We can convert 9000 rev/min to rad/sec (proper units for angular velocity) using dimensional analysis.
[tex]\frac{9000rev}{min} * \frac{min}{60 s}* \frac{2\pi rad}{1 rev} = \boxed{942.48 rad/sec}[/tex]
b)
For the mass to go around at this speed, we can use the rotational equivalent for centripetal force:
[tex]F_c = m\omega ^2r[/tex]
Plug in the given values. Remember to convert grams to kg.
[tex]F_c = (0.01)(942.48^2)(0.20) = \boxed{1776.53 N}[/tex]
c)
The force is a CENTRIPETAL force, so it must act towards the CENTER of the circle at all times.
d)
The only force working in the horizontal direction on the mass is:
[tex]\Sigma F = F_c = F_N[/tex]
The normal force from the container's walls provide the centripetal force experienced by the mass.
e)
When the ball is at rest, the force supplied by the earth is equivalent to its weight:
[tex]W = mg[/tex]
Plug in the givens:
[tex]W = (0.01)(9.8) = \boxed{0.098 N}[/tex]
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