Frequency Arc
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Circular Motion Questions! HELP!!!?
Question #1:
The "vomit comet", an airplane used to train astronauts in a "weightless" environment, travels at a speed of 200 m/s. The trajectory of the plane is a large circular arc. What radius would produce a weightless environment for a 80 kg astronaut?
Question #2:
A popular amusement park ride is "the rotator", a large cylinder in which the riders stand on the inside and press themselves against the inner wall. The cylinder begins to spin about its central axis and at a specific rotational rate, the bottom drops out of the cylinder. Some strange force "glues" the riders to the inner wall so that they don't drop out. A typical cylinder has a diameter of 8 m. If the coefficient of friction between the rider and the wall is 0.5, at what frequency, f, should the ride rotate at so that no rider slips down the inner wall?
Please help~~!!!! Don't have a clue on where to even start...
Problem 1: The assumption is that the plane motion will create a centrifigual force that exactly counters gravity. The mass of the astronaut makes no difference.
g =v^2/r => r = v^2/g= 200^2 /9.8 = 4079 meters
Problem 2: The force of friction between the rider and the side must cancel the force of gravity. To hold the person against the side wall requires a frictional force of M*g, with M being the mass of the person With a coefficient of friction equal to 0.5, the centrigual force must be
Fcent*mu=M*g.=> Fcent=M*g/mu
We can write the force on the rider as follows.
Fcent= M*w^2 r=> w = (M*g/mu*M*r)^0.5 = 2.215 radians/sec
f = w/2*pi = 2.215/6.28 = 0.35 Hz
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