Question

Small birds can migrate over long distances without feeding, storing energy mostly as fat rather than carbohydrate. 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 1 Cal = 4186 J.

Part A

Consider a bird that flies at an average speed of 10.7 m/s and releases energy from its body fat reserves at an average rate of 3.70 W (this rate represents the power consumption of the bird). Assume that the bird consumes 4g of fat to fly over a distance d_b without stopping for feeding. How far will the bird fly before feeding again?
Express your answer in kilometers.

Part B

How many grams of carbohydrate m_carb would the bird have to consume to travel the same distance d_b?
Express your answer in grams

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 800 km. Assuming that the bird has an average speed of 40.0 km/hr and an average power consumption of 1.70 W, how many grams of fat does a ruby-throated hummingbird need to accomplish the nonstop flight across the Gulf of Mexico?
Express your answer in grams.

Answer 1

Part A ANSWER

The problem tells us that one gram of fat has 9.4 Calories. Each Calorie equals 4186 J, so that means a gram of fat contains about 39,348 J of energy, and 4 grams of fat has about 157,394 J of energy. One Watt is equal to 1 joule per second, so a bird that burns energy at a rate of 3.7 W is burning 3.7 joules a second. This means it can fly for about 42,539 seconds (157,394 / 3.7). At a speed of 10.7 m/s, it will fly for about 455,165 m, which equals 455.165 km.

455.165 km

Part B ANSWER

The problem tells you that one gram of fat has about 9.4 Calories of energy, compared to 4.2 for a gram of carbs. So there is 2.2381 times as much energy in a gram of fat. If the bird consumes 4 grams of fat during its flight, it would have to consume 2.2381 * 4 = 8.9523 grams of carbs.

8.9523 g

Part C ANSWER

To fly 800 km will take about 20 hours (at 40km/hr). This is equal to 72,000 seconds. At a power consumption of 1.7 W, the bird will consume (1.7 * 72,000) 122,400 J of energy. Since a gram of fat contains about (9.4 Calories * 4186 J/Calorie) 39348 joules of energy, the bird will need (122,400 / 39,348) about 3.1107 grams of fat.

3.1107 g