A roller coaster at the Six Flags Great America amusement park in Gurnee, Illinois, incorporates some clever design technology and some basic physics. Each vertical loop, instead of being circular, is shaped like a teardrop (Fig. P6.13). The cars ride on the inside of the loop at the top, and the speeds are fast enough to ensure the cars remain on the track. The biggest loop is 40.0 m high. Suppose the speed at the top of the loop is 13.0 m/s and the corresponding centripetal acceleration of the riders is 2g. (a) What is the radius of the arc of the teardrop at the top? (b) If the total mass of a car plus the riders is M, what force does the rail exert on the car at the top? (c) Suppose the roller coaster had a circular loop of radius 20.0 m. If the cars have the same speed, 13.0 m/s at the top, what is the centripetal acceleration of the riders at the top? (d) Comment on the normal force at the top in the situation described in part (c) and on the advantages of having teardrop-shaped loops.
A roller coaster at the Six Flags
Great America amusement park
in Gurnee, Illinois, incorporates
some clever design technology
and some basic physics. Each vertical
loop, instead of being circular,
is shaped like a teardrop
(Fig. P6.13). The cars ride on
the inside of the loop at the top,
and the speeds are fast enough
to ensure the cars remain on the
track. The biggest loop is 40.0 m
high. Suppose the speed at the
top of the loop is 13.0 m/s and
the corresponding centripetal
acceleration of the riders is 2g. (a) What is the radius of the
arc of the teardrop at the top? (b) If the total mass of a car
plus the riders is M, what force does the rail exert on the car
at the top? (c) Suppose the roller coaster had a circular loop
of radius 20.0 m. If the cars have the same speed, 13.0 m/s
at the top, what is the centripetal acceleration of the riders
at the top? (d) Comment on the normal force at the top in
the situation described in part (c) and on the advantages of
having teardrop-shaped loops.
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