Question

An apple with a mass of 0.49 kg falls 4 meters from the top of a tree and hits the ground 2 seconds later. What is the force of air resistance on the apple?

Answer 1

Force of air resistance = 3.822 N

Explanation:

I think the question you have asked is bit more complex than it looks. When apple starts falling it gains velocity and its velocity increases due to acceleration due to gravity of earth. But the force of air resistance is directly proportional to the velocity of the body in consideration (here apple). Hence, the apple will be in a non uniformly accelerated motion.
But Newtonian equations of motion are valid only for moving bodies in uniform acceleration.
But to calculate the answer we are assuming constant acceleration. Then
By second equation of motion,
`s=ut+1/2at^2`
Here, s = h = 4 m
u = 0
t = 2 s
Substitute the above values in the equation,
`a=(2h)/t^2= 2*4/2^2=2m/s^2`
This is the net acceleration of the apple due to two opposing forces (1) gravitational force of earth
(2) air resistance
Upward acceleration due to air resistance = g-a = 9.8-2 = 7.8 `m/s^2`
Force of air resistance = (mass of apple) (upward acceleration) = `0.49*7.8=3.822N`