A 1.80-g hailstone, which can be modeled as a particle, falls a vertical distance of 155 m at constant speed. What is the work done on the hailstone by gravity and air resistance?
(a) gravity
J
(b) air resistance
J
It is at terminal velocity, constant speed, so the net force on it is zero.
There is a force down, -m g if plus is up
There is a friction force up, + mg if negative is down
It moves down, -150 meters
so
Work done by g = - m g (-150 ) = +150 m g Joules
Work done by friction = +mg (-150) = -150 m g Joules
m = 0 .0018 kg and g = 9.8 m/s^2
To find the work done on the hailstone by gravity and air resistance, we need to calculate the work done by each force separately.
(a) Work done by gravity:
The work done by gravity can be calculated using the formula: Work = Force × Distance × cos(θ), where θ is the angle between the force and the displacement.
In this case, the force of gravity is acting vertically downwards, and the displacement is also vertical. Therefore, the angle between the force and displacement is 0 degrees (cos(0) = 1).
The formula for work becomes: Work_gravity = Force_gravity × Distance
The force of gravity can be calculated using the formula: Force_gravity = mass × acceleration due to gravity (g)
Given that the mass of the hailstone is 1.80 g (convert to kg: 1.80 g × 0.001 kg/g = 0.0018 kg) and the acceleration due to gravity is approximately 9.8 m/s², the force of gravity is: Force_gravity = 0.0018 kg × 9.8 m/s² = 0.01764 N
The distance over which the hailstone falls is given as 155 m.
Substituting the values into the formula: Work_gravity = 0.01764 N × 155 m = 2.73 J
Therefore, the work done on the hailstone by gravity is 2.73 J.
(b) Work done by air resistance:
The work done by air resistance can be calculated using the formula: Work = Force × Distance × cos(θ), where θ is the angle between the force and the displacement.
In this case, the force of air resistance is acting in the opposite direction to the displacement, which makes the angle between them 180 degrees (cos(180) = -1).
The formula for work becomes: Work_air resistance = Force_air resistance × Distance × cos(180)
The force of air resistance is difficult to calculate without additional information about the shape and properties of the hailstone. It depends on factors like the shape, cross-sectional area, and velocity of the hailstone.
Without this information, it can be assumed that the work done by air resistance is negligible or zero if the hailstone is assumed to have a small cross-sectional area and a relatively low velocity.
Therefore, the work done on the hailstone by air resistance is assumed to be zero or negligible.