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## Investigation Activity 4

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**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