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The maximum lift force on a bat is proportional to the square of its flying speed v. For the hoary bat (Lasiurus cinereus), the magnitude of the lift force is given by

The bat can fly in a horizontal circle by “banking” its wings at an angle θ, as shown in Figure P7.72. In this situation, the magnitude of the vertical component of the lift force must equal the bat’s weight. The horizontal component of the force provides the centripetal acceleration.

(a) What is the minimum speed that the bat can have if its mass is 0.031 kg?

(b) If the maximum speed of the bat is 10 m/s, what is the maximum banking angle that allows the bat to stay in a horizontal plane?

(c) What is the radius of the circle of its flight when the bat flies at its maximum speed?

(d) Can the bat turn with a smaller radius by flying more slowly?

Figure P7.72: