Please answer both parts 1) A space station shaped like a giant wheel has a radi
ID: 1775956 • Letter: P
Question
Please answer both parts
1) A space station shaped like a giant wheel has a radius of 147 m and a moment of inertia of 5.15 108 kg · m2. A crew of 150 lives on the rim, and the station is rotating so that the crew experiences an apparent acceleration of 1g. When 100 people move to the center of the station for a union meeting, the angular speed changes. What apparent acceleration is experienced by the managers remaining at the rim? Assume that the average mass of each inhabitant is 65.0 kg.
2) The pressure at the bottom of a glass filled with water ( = 1000 kg/m3) is P. The water is poured out and the glass is filled with mercury ( = 13.6 103 kg/m3). The pressure at the bottom of the glass is now which of the following?
smaller than P
larger than P
indeterminate
equal to P
Explanation / Answer
1)
acceleration a1 = r*w1^2 = 1g = 9.8 m/s^2
w1 = sqrt(a1/r)
initial angular momentum Li = (I+I1)*w1 = (I + n1*m*r^2)*w1 = ( I + n1*m*r^2)*sqrt(a1/r)
after 100 people moved to meeting
final angular momentum Lf = (I+I2)*w2 = (I + n2*m*r^2)*sqrt(a2/r)
from conservation of angular momentum
Lf = Li
(I + n2*m*r^2)*sqrt(a2/r) = ( I + n1*m*r^2)*sqrt(a1/r)
(5.15*10^8 + (150*65*147^2))*sqrt(g/147) = (5.15*10^8 + (50*65*147^2))*sqrt(a2/147)
aceeleration experienced a2 = 1.54 g <<<-----ANSWER
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pressure at the bottom P = Po + rho_water*g*h
Po = atmospheric pressure
when filled with water
P1 = Po + rho_mercury*g*h
since rho_mercury(13.6*1000) is greater than rho_water(1000)
largerthan P