22. QC A roller coaster at the Six Flags Great America amusement park in Gurnee, llinois, incorpo rates some clever design technol ogy and some basic physics. Each vertical loop, instead of being circular, is shaped like a teardrop (Fig. P5.22). The cars ride on the inside of the loop at the top, and the speeds are fast enough to en- sure 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 cor responding 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 cen- tripetal 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 Figure P5.22 Frank Cezus/Getty Images

Question
22. QC A roller coaster at the Six
Flags Great America amusement
park in Gurnee, llinois, incorpo
rates some clever design technol
ogy and some basic physics. Each
vertical loop, instead of being
circular, is shaped like a teardrop
(Fig. P5.22). The cars ride on the
inside of the loop at the top, and
the speeds are fast enough to en-
sure 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 cor
responding 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 cen-
tripetal 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
Figure P5.22
Frank Cezus/Getty Images

Image Transcription

22. QC A roller coaster at the Six Flags Great America amusement park in Gurnee, llinois, incorpo rates some clever design technol ogy and some basic physics. Each vertical loop, instead of being circular, is shaped like a teardrop (Fig. P5.22). The cars ride on the inside of the loop at the top, and the speeds are fast enough to en- sure 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 cor responding 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 cen- tripetal 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 Figure P5.22 Frank Cezus/Getty Images

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