mass m
force down = m g
centripetal force = m v^2/R
tan 30 = (v^2/R) / g
but R = 8 + 24 sin 30 = 8 +12 = 20 feet radius total
tan 30 = 0.577 = (v^2 /20) / 32
v^2 = 369 ft/s
v = 19.2 ft/s
time for one rev = 2 pi R /v = 40 pi /19.2 = 62.8 s
about 1 rev / min
In a amusement park ride, gondola cars of weight W are attached by rods 24ft long to a bull
wheel 16ft in diameter. The bull wheel rotates in a horizontal plane about a vertical axis at its
center. At how many rpm is it rotating when the supporting rods of the gondolas are inclined at
30° with the vertical? Consider each gondola to be a particle concentrated at the end of each
24ft rod.
1 answer
1 answer