Suppose a 300–g kookaburra (a large kingfisher bird) picks up a 77.0–g snake and raises it 2.70 m from the ground to a branch. How much work did the bird do on the snake?
How much work did it do to raise its own center of mass to the branch?
F = M*g = 0.077 * 9.8 = 0.755 N.
Work = F*d.
To calculate the work done by the kookaburra on the snake and on itself, we need to use the formula:
Work = Force × Distance × cos(θ)
For the kookaburra lifting the snake:
1. Determine the force exerted by the kookaburra on the snake. The force can be calculated using the formula:
Force = mass × acceleration due to gravity
The mass of the snake is 77.0 g, which is 0.077 kg. The acceleration due to gravity is approximately 9.8 m/s².
Force = 0.077 kg × 9.8 m/s²
2. Calculate the distance the snake was raised, which is given as 2.70 m.
3. Since the force and distance are both vertical, the angle θ between them and the direction of motion is 0 degrees. The cosine of 0 degrees is 1.
Work = Force × Distance × cos(θ)
Plug in the values:
Work = (0.077 kg × 9.8 m/s²) × 2.70 m × 1
Simplify the equation:
Work = 2.0094 Joules (rounded to four decimal places)
So, the kookaburra did approximately 2.0094 Joules of work on the snake.
For the kookaburra lifting itself:
1. Determine the force exerted by the kookaburra on itself. The force can be calculated using the formula:
Force = mass × acceleration due to gravity
The mass of the kookaburra is 300 g, which is 0.300 kg. The acceleration due to gravity is approximately 9.8 m/s².
Force = 0.300 kg × 9.8 m/s²
2. Calculate the vertical distance the kookaburra raised itself, which is also given as 2.70 m.
3. Similar to the previous case, the angle θ between the force and distance is 0 degrees, and the cosine of 0 degrees is 1.
Work = Force × Distance × cos(θ)
Plug in the values:
Work = (0.300 kg × 9.8 m/s²) × 2.70 m × 1
Simplify the equation:
Work = 7.722 Joules
Therefore, the kookaburra did approximately 7.722 Joules of work to raise its own center of mass to the branch.