Passengers riding in the Great Six Flags Air Racer are spun around a tall steel

Question

Passengers riding in the Great Six Flags Air Racer are spun around a tall steel tower (see the figure). At top speed the planes fly at a 59.0 obank approximately 16.0 m from the tower. In this position the support chains make an angle of 59.0 o with the vertical. Calculate the speed of the planes.

Passengers riding in the Great Six Flags Air Racer are spun around a tall steel tower (see the figure). At top speed the planes fly at a 59.0 bank approximately 16.0 m from the tower. In this position the support chains make an angle of 59.0 o with the vertical. Calculate the speed of the planes.

Explanation / Answer

The tension in the cable comes from solving the vertical forces

T*cos(59) = m*g

so T = m*g/cos(59)

Now sum horizontal forces

T*sin(59) = m*v^2/r

so m*g/cos(59)*sin(59)= m*v^2/r

so v = sqrt(tan(59)*g*r) = sqrt(tan(59)*9.8*16) = 16.15m/s

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