Question

The smallest bird is the Cuban bee hummingbird, which has a mass of only 1.7 g. If this bird did 8.8 10 –4J of work by exerting an upward force of 3.4 10 –4 N, how far did it fly?

Answer 1

The distance the bird flew is approximately 2.59 meters

Step-by-step explanation:

We list out the parameters in the question, and the required measurement as follows;

The mass of the Cuban bee hummingbird, m = 1.7 g = 0.0017 kg

The amount of work the bird does, W = 8.8 × 10⁻⁴ J

The amount of upward force the bird exerts, F = 3.4 × 10⁻⁴ N

Let 'd' represent the distance flown by the bird

(The downward force,
`F_g` = The weight of the bird, W

W = The mass of the bird, m × The acceleration due to gravity, g

The acceleration due to gravity, g ≈ 9.81 × 10 m/s²

∴
`F_g` ≈ 0.0017 kg × 9.81 m/s² = 0.016677 N > F)

Given that the weight of the bird is larger than 'F', we assume that the force exerted by the bird is the net force,
`F_(NET)` = F

Therefore;

Work done, W = Net Force,
`F_(NET)` × Distance, d

∴ W =
`F_(NET)` × d

d = W/
`F_(NET)` = 8.8 × 10⁻⁴ J/(3.4 × 10⁻⁴ N) = 2.58823529 meters

The distance the bird flew, d ≈ 2.59 m.