How Is Work Done by Air Resistance Calculated in a Falling Raindrop Scenario?

[PepeF.]

Homework Statement

a .459kg raindrop falls vertically at constant speed under the influence of gravity and air resistance. acceleration due to gravity is 9.8 m/s

after the drop 141 m, the work done by gravity is 634.246 J

a problem ask the work donde by air resistance
the work done by gravity is 634.246J

Homework Equations

i just know regular force and work

w=f*change in x/y
f= m*g

The Attempt at a Solution

i don't know what to do

 

[tiny-tim]

Hi PepeF.!

Hint: use the work-energy theorem …

total work done = change in kinetic energy ​

 

[kerimek]

I would approach this problem by first understanding the concept of work done by air resistance. Air resistance is a type of frictional force that opposes the motion of an object through air. It acts in the opposite direction of the object's motion, and its magnitude depends on the speed and surface area of the object.

To find the work done by air resistance in this scenario, we can use the formula W = Fd, where W is work, F is the force, and d is the distance. In this case, the force is the air resistance and the distance is the distance the raindrop has traveled. However, we need to find the value of the air resistance force.

To do this, we can use the formula for air resistance force, F = 0.5*p*Cd*A*v^2, where p is the density of air, Cd is the drag coefficient, A is the surface area of the raindrop, and v is the velocity of the raindrop. Since the raindrop is falling at a constant speed, we can assume that the force of air resistance is equal to the force of gravity, which is mg.

Substituting the values given in the problem, we get:

F = 0.5 * 1.225 kg/m^3 * 0.47 * (pi*0.05^2) * (9.8 m/s)^2 = 0.058 N

Now, we can plug this value into the formula for work done by air resistance:

W = Fd = 0.058 N * 141 m = 8.178 J

Therefore, the work done by air resistance is 8.178 J. This value is much smaller than the work done by gravity, which makes sense since the raindrop is falling at a constant speed. The majority of the work done is by gravity, while air resistance only plays a small role.