Question

Small birds can migrate over long distances without feeding, storing energy mostly as fat rather than carbohydrate. (Figure 1) Fat is a good form of energy storage because it provides the most energy per unit mass: 1 gram of fat provides about 9.4 (food) Calories, compared to 4.2 (food) Calories per 1 gram of carbohydrate. Remember that Calories associated with food, which are always capitalized, are not exactly the same as calories used in physics or chemistry, even though they have the same name. More specifically, one food Calorie is equal to 1000 calories of mechanical work or 4186 joules. Therefore, in this problem use the conversion factor 1Cal=4186J.



Part C

Field observations suggest that a migrating ruby-throated hummingbird can fly across the Gulf of Mexico on a nonstop flight traveling a distance of about 800km . Assuming that the bird has an average speed of 40.0km/hr and an average power consumption of 1.70W , how many grams of fat mfat does a ruby-throated hummingbird need to accomplish the nonstop flight across the Gulf of Mexico?

Express your answer in grams.

Answer 1

Let d = distance (in m) to be covered by the bird before stopping for feeding again.

Time to fly this distance = d/(10.7) sec.

Energy used = 3.70 * d/(10.7) J

Equate to the energy equivalent of 4 g fat

=> 3.70 * d/(10.7) = 4 * (9.4) * 4186

=> d = [4 * (9.4) * 4186] / [(3.70) * (10.7)]

=> d = 3976 m

=> d = 3.976 km.

Edit:

Amount of carbohydrate needed = 4 * (9.4/4.2) = 8.95 g.

Let the ruby-throated hummingbird need x g of fat

=> energy used = x * 9.4 * 4186 J

Time to fly 800 km

= 800/40 * 3600 sec = 72000 sec

By energy balance,

1.7 * 72000 = x * 9.4 * 4186

=> x

= (1.7 * 72000) / (9.4 * 4186) g

= 3.11 g