Speed Storm
Speed Storm
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What is the mass of air in 1.0 km3 of air moving at a speed of 300km/h?
In a tropical storm, wind speeds of up to 300km/h. Calculate the energy contained in 1.0 km3 of air moving at this speed.
please explain each step you take including the coversions.
kinetic energy, KE, is 1/2 mv^2, you are given the speed (we should convert it to m/s; 1 km/hr = 0.28 m/s, so 300 km/h = 83.3 m/s)
the density of air is about 1.2 kg/m³, now the density of air depends on T and humidity, the value I quote is for dry air (certainly not the case here) for 20C; so this number is not precise, but will serve to give you a close approx
so, we need to know the mass in 1km³
there are 10^3 m in a km, and a km³ is 1000m x 1000m x 1000m or 10^9m³
so 1 km³ has a mass of
1.2 kg/m³ x 10^9 m³ = 1.2x10^9 kg
the kinetic energy of this volume of air is then:
KE=1/2 x 1.2x10^9 kg x (83.3 m/s)²
=4.16x10^12 J...which is a lot of energy!!