Question

A coffee filter of mass 1.4 grams dropped from a height of 4 m reaches the ground with a speed of 0.9 m/s. How much kinetic energy Kair did the air molecules gain from the falling coffee filter? Start from the Energy Principle, and choose as the system the coffee filter, the Earth, and the air.

Answer 1

The kinetic energy gained by the air molecules is 0.054313 J.

Step-by-step explanation:

Given that,

Mass of a coffee filter, m = 1.4 g

Height from which it is dropped, h = 4 m

Speed at ground, v = 0.9 m/s

Initially, the coffee filter has potential energy. It is given by :

`P=mgh\\\\P=1.4* 10^(-3)\ kg* 9.8\ m/s^2* 4\ m\\\\P=0.05488\ J`

Finally, it will have kinetic energy. It is given by :

`E=(1)/(2)mv^2\\\\E=(1)/(2)* 1.4* 10^(-3)* (0.9)^2\\\\E=0.000567\ J`

The kinetic energy Kair did the air molecules gain from the falling coffee filter is :

`E=0.000567-0.05488=0.054313\ J`

So, the kinetic energy Kair did the air molecules gain from the falling coffee filter is 0.054313 .