Rotating Space Station

Classical Mechanics Level 2

For an interstellar space mission,set in the future,an attempt is made to partially compensate for the lack of gravity by uniformly rotating the reasonably long and very heavy cylindrical spaceship , which has diameter of 2R=20m around its symmetry axis . The period of rotation is adjusted so that astronauts feel an earth like gravitational acceleration of g=10.00 at the outer edges of cylinder During the journey,an astronaut(point like!) climbs a 5m pole whose floor is the innersurface of the space ship. if the astronaut fell from top of the pole a) How long would he take to fall(in sec) b)How far from the bottom of the climbing pole(measured along the floor) would he hit the floor ENTER THE SUM OF ANSWERS OF (a) AND (b)


The answer is 8.5805.

Dark Angel by DARK ANGEL , 14, India

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1 solution

Steven Chase
May 25, 2020

This was a fun problem. Commented solution code is attached: 

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import math

R = 10.0         # circle radius
g = 10.0         # artificial gravity strength

# g = R*(w**2.0)
w = math.sqrt(g/R)  # angular speed from centripetal force

#############################

# Calculate fall to inner surface

x = 0.0     # coordinates of ladder top when astronaut begins to fall
y = -5.0

v = 5.0*w   # initial astronaut speed

# x**2.0 + y**2.0 = R**2.0

xc = math.sqrt(R**2.0 - y**2.0)  # collision x coordinate

t = xc/v                     # time of fall

theta1 = math.atan2(y,xc)    # angle of impact point

#############################

# Determine distance between points of interest

theta2 = -math.pi/2.0 + w*t  # ladder starts at -pi/2 radians
                            # and advances by w*t

d = R*math.fabs(theta1 - theta2)  # distance between ladder base.....;
                                    # and astronaut when he lands

#############################

print (theta1*180.0/math.pi)    # angle of landing position in degrees
print (theta2*180.0/math.pi)    # angle of ladder base at landing instant (degrees)

print ""

print t            # print falling time
print d            # print distance between landing position and ladder base
print (t + d)       # sum of both numbers


# Results

#>>> 
#-30.0
#9.23920117592

#1.73205080757
#6.84853256372
#8.58058337129
#>>>

3 Helpful 3 Interesting 3 Brilliant 0 Confused

@Steven Chase thanks for the solution,I would advice u to solve the problem wrt spaceship frame to make it more interesting

DARK ANGEL - 1 year ago

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