Question

A coffee filter of mass 1.2 grams dropped from a height of 1 m reaches the ground with a speed of 0.8 m/s. How much kinetic energy 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

Answer: The energy gained by the air molecules is 0.011 J.

Explanation:

Law of conservation of energy states that energy can neither be created nor be destroyed but it can only be transformed from one form to another form.

Here, the potential energy of the coffee filter is getting converted into kinetic energy of the coffee filter and some energy is lost by it which is gained by the air molecules in the form of kinetic energy.

So, calculating the potential energy of coffee filter, we use the equation:

P = mgh

where,

m = mass of coffee filter = 1.2 g = $1.2\times 10^{-3}kg$    (Conversion used: 1 kg = 1000 g)

g = acceleration due to gravity = $9.8m/s^2$

h = height of coffee filter = 1 m

Putting values in above equation, we get:

$P=1.2\times 10^{-3}kg\times 9.8m/s^2\times 1m\\\\P=1.176\times 10^{-2}J$

• Calculating the kinetic energy of coffee filter, we use the equation:

$E=\frac{1}{2}mv^2$

where,

m = mass of coffee filter = 1.2 g = $1.2\times 10^{-3}kg$

v = speed of coffee filter = 0.8 m/s

Putting values in above equation, we get:

$E=\frac{1}{2}\times 1.2\times 10^{-3}kg\times (0.8m/s)^2\\\\E=3.84\times 10^{-4}J$

As, energy lost by coffee filter = energy gained by air molecules

So, energy lost by coffee filter = Potential energy - Kinetic energy

Energy lost by coffee filter = $(1.176\times 10^{-2})-(3.84\times 10^{-4})=0.011J$

Hence, the energy gained by the air molecules is 0.011 J.