Problem: Calculate the energy involved in an asteroid impact Asteroid Characteristics: Spherical, iron-nickel with density of 7800 kg/m3 Diameter 40 meters Velocity 20,000 meters/second
Energy equation for a moving object: KE = ½ mv2 Kinetic Energy = KE Mass = m Velocity = v
What do we need to know to solve the problem? KE = ½ mv2 We are solving for KE, so we need what two things?
Mass and Velocity Here is what we have been given: • Spherical, iron-nickel with density of 7800 kg/m3 • Diameter 40 meters • Velocity 20,000 meters/second
Velocity Velocity is the speed and direction an object is moving This is easy they gave it to us directly as v = 20,000 meters per second
Mass They didn’t give us this directly. How can we figure out the total mass of the asteroid from what they did give us? Spherical, iron-nickel with density of 7800 kg/m3 Diameter 40 meters
Density and Diameter Density tells us how much mass is a cubic meter Diameter will let us calculate the volume of the asteroid in cubic meters Can this get us to total mass?
Density • Density is how tightly packed the matter in an object is: mass/volume • Which is denser a rock or a marshmallow of the same size
Density • Mass is the amount of matter in an object measured in grams • Volume is the amount of space an object takes up measured in mL or cm3
(1 a) Calculate Volume: Find the volume of the asteroid: Remember it is a spherical asteroid… V = (4/3) × pi × r3Use pi = 3.14
Calculate for our Asteroid 40 meters in diameter Our volume formula uses radius What is the radius of our asteroid?
Time to plug in our #’s V = (4/3) × pi × r3 Radius = 20 m Pi = 3.14 So, 203 = 8,000 m3 Volume = (4/3) x 3.14 x 8,000 m3
Volume is…. 33,510 m3 = (4/3) x 3.14 x 8,000 m3
(1 b) Find the Total Mass Multiply the volume by density: • Density = 7800 kg/m3 (given) • Volume = 33,510 m3 (calculated) 33,510 m3 x 7800 kg/m3 =
(1 b) Total Mass is… 261,378,000 kg = 33,510 m3 x 7800 kg/m3
(1 c) Energy of the Asteroid KE = ½ mv2 Mass = 261,378,000 kg (calculated) Velocity = 20,000 m/s (given) (20,000 m/s)2 = 400,000,000 m/s2
Time to plug in #’s again KE = ½ x 261,378,000 kg x 400,000,000 m/s2
(1 c) The Energy is… KE = 5.228 x 1016 Joules Joules are kg*m/s2 Or about the energy needed to lift a quarter pound hamburger straight up one meter in one second