Problem 2. Hummingbirds use their long tongues to collect floral nectar (Fig. 2a-b). The distal portion of the bird's tongue consists of thin keratinized membrane that spontaneously folds into two conjoining tubes when extended (Fig. 2c-d). Additionally, hummingbirds have no muscular control over the shape of its tongue and active suction is impossible; instead, they rely on capillarity to drive up the nectar. Once the tongue is loaded with nectar, it is retracted into the bill for ingestion. Given nectar has a density of p= 1060 kg/m, surface tension of 0.052 N/m, the contact angle between the hummingbird's tongue and nectar is = 30, determine the maximum volume of nectar the hummingbird can imbibe each time it dips into the jar (Fig. 3). (a) (c) Air (b) a Nectar 50 ms (d) Cross section Posterior view Figure 2: (a) Hummingbirds drink nectar, a sweet liquid inside certain flowers. (b) Anatomy of hummingbirds. (c) Hummingbird's tongue spontaneuously folds into two conjoining tubes when extended. (d) Cross-sectional view of the hummingbird tongue. Scale bars are 0.5 mm. Figure 3: A hummingbird drinking nectar at an angle a = 65.