Question

A 20.0-kg package is dropped from a high tower in still air and is "tracked" by a radar system. When the package is 25 m above the ground, the radar tracking indicates that its acceleration is 7.0 m/s2. Determine the force of air resistance on the package.

Answer 1

Answer:

56 N

Explanation:

There are only two forces acting on the package:

- The force of gravity, directed downward, equal to

$mg$

where m is the mass of the package and g is the acceleration due to gravity

- The air resistance, acting upward, let's label it with $R$

According to Newton's second law, the resultant of the two forces must be equal to the product between the mass, m, and the acceleration, a:

$mg-R=ma$

where we have:

m = 20.0 kg

g = 9.8 m/s^2

a = 7.0 m/s^2 is the acceleration when the package is at 25 m above the ground.

Substituting into the equation, we can find the magnitude of the air resistance at that altitude:

$R=mg-ma=m(g-a)=(20.0 kg)(9.8 m/s^2-7.0 m/s^2)=56 N$