Consider a drop of mass 1g falling from a height 1km.what is work done by gravity?
To find the work done by gravity on the drop, we can use the formula:
Work = Force × Distance × cos(θ)
In this case, the force is the weight of the drop, which can be calculated using the formula:
Force = mass × acceleration due to gravity
The acceleration due to gravity is approximately 9.8 m/s^2. However, we need to convert the mass from grams to kilograms by dividing it by 1000.
So, the weight of the drop is:
Weight = (1g ÷ 1000) kg × 9.8 m/s^2
Next, we need to calculate the distance the drop falls. You mentioned that the height is 1 km, which is 1000 meters.
Now, we can calculate the work done by gravity:
Work = Weight × Distance × cos(θ)
Since the drop is falling vertically downward, the angle θ between the force and distance is 0 degrees. Therefore, cos(θ) is equal to 1.
Work = Weight × Distance × 1
Substituting the values:
Work = (1g ÷ 1000) kg × 9.8 m/s^2 × 1000 m × 1
Simplifying the equation:
Work = 1 kg × 9.8 m/s^2 × 1000 m
Work = 9800 Joules
Therefore, the work done by gravity on the 1g drop falling from a height of 1km is 9800 Joules.
work = m g h
in real life, terminal velocity becomes a factor