A 3.56 x 10-5 kg raindrop falls vertically at constant speed under the influence of gravity and air resistance. After the drop has fallen 83.8 m, what is the work done by gravity? Answer in units of milliJoule (a thousandth of a Joule) and use 9.8 m/s2 for g.
To find the work done by gravity, we can use the formula:
Work = Force × Distance
The force due to gravity can be calculated using the formula:
Force = mass × acceleration
Given:
mass of the raindrop = 3.56 x 10^-5 kg
acceleration due to gravity = 9.8 m/s^2
distance = 83.8 m
First, let's calculate the force due to gravity:
Force = mass × acceleration
= (3.56 x 10^-5 kg) × (9.8 m/s^2)
= 3.4928 x 10^-4 N
Now, we can calculate the work done by gravity:
Work = Force × Distance
= (3.4928 x 10^-4 N) × (83.8 m)
= 0.0292 J
Since we need the answer in milliJoule, we can convert it:
0.0292 J = 29.2 milliJoule
Therefore, the work done by gravity is 29.2 milliJoule.
To find the work done by gravity, we need to calculate the gravitational force acting on the raindrop and then multiply it by the distance it has fallen.
The gravitational force can be calculated using the formula:
F_gravity = mass x acceleration due to gravity
Given:
Mass of the raindrop (m) = 3.56 x 10^-5 kg
Acceleration due to gravity (g) = 9.8 m/s^2
Plugging these values into the formula, we get:
F_gravity = 3.56 x 10^-5 kg x 9.8 m/s^2
Next, we need to calculate the work done by multiplying the force by the distance:
Work = force x distance
The distance fallen (d) = 83.8 m
Plugging in the values, we get:
Work = F_gravity x d
Now let's calculate the work done by gravity in milliJoules:
Work = (3.56 x 10^-5 kg x 9.8 m/s^2) x 83.8 m
Work = 0.03499552 Joules
Since we need the answer in milliJoules (thousandth of a Joule), we multiply by 1000:
Work = 34.99552 milliJoules
Therefore, the work done by gravity on the raindrop after falling 83.8 m is approximately 34.996 milliJoules.