Answer:
The work performed by air resistance totals -0.0782 J
Explanation:
Hello!
According to the principle of conservation of energy, the energy of a raindrop must remain constant.
At the outset, the raindrop possesses only gravitational potential energy:
PE = m · g · h
Where:
PE = potential energy.
m = mass of the raindrop.
g = gravitational acceleration (9.8 m/s²)
h = height.
Let's determine the initial potential energy of the raindrop:
(4 mg should be converted into kg: 4 mg · 1 kg / 1 × 10⁶ mg = 4 × 10⁻⁶ kg)
PE = 4 × 10⁻⁶ kg · 9.8 m/s² · 2000 m
PE = 0.0784 J
As the raindrop descends, some of its potential energy converts into kinetic energy while the rest is lost to the air resistance. Upon reaching the ground, all initial potential energy has been either turned into kinetic energy or spent overcoming air resistance:
initial PE = final KE + Work by air
Where:
KE = kinetic energy.
Work by air = work done by air resistance.
The kinetic energy at ground level is computed as follows:
KE = 1/2 · m · v²
Where:
m = mass
v = velocity
<pThus:
KE = 1/2 · 4 × 10⁻⁶ kg · (10 m/s)²
KE = 2 × 10⁻⁴ J
Now, we can find the work done by air resistance:
initial PE = final KE + Work by air
0.0784 J = 2 × 10⁻⁴ J + Work by air
Work by air = 0.0784 J - 2 × 10⁻⁴ J
Work by air = 0.0782 J
Since work is performed in the opposite direction to movement, this results in a negative value. Therefore, the work done by air resistance is -0.0782 J.
