Question

A 10 kg migratory swan cruises at 20 m/s. A calculation that takes into ac- count the necessary forces shows that this motion requires 200 W of mechanical power. If we assume an efficiency similar to humans (say, 25%), a reasonable assumption, then the metabolic power of the swan is significantly higher than this. The swan does not stop to eat during a long day of flying; it get the energy it needs from fat stores. Assuming an efficiency similar to humans, after 12 hours of flight, a. How far has the swan traveled? b. What fraction of its body mass does it lose? Assume that I g of fat contains 37 kJ of energy.

Answer 1

Answer:

total distance moved by the swan is

d = 864000 m

Fraction of total mass lost by it

$fraction = 0.0934$

Explanation:

As we know that swan cruises at 20 m/s speed

Part a)

Distance moved by the swan is product of speed and time

so we have

$d = v t$

$d = 20 \times (12 \times 3600)$

$d = 864000 m$

Part b)

As we know that power consumed by the swan is 200 W

so total energy consumed in 12 hours is given as

$E = P \times t$

$E = 200(12 \times 3600)$

$E = 8.64 \times 10^6 J$

Since we know that output power is 25% of total energy used so total energy consumed is given as

$E_{net} = 3.456 \times 10^7 J$

now we know that 1 g of fat is lost for 37 kJ energy

so total mass lost in this

$m = \frac{3.456\times 10^7}{37 \times 10^3}$

$m = 934 g$

so fraction of mass lost is given as

$fraction = \frac{0.934}{10}$

$fraction = 0.0934$