Investigation Activity 4. Problem: Calculate the energy involved in an asteroid impact Asteroid Characteristics: Spherical, iron-nickel with density of.

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Presentation transcript:

Investigation Activity 4

Problem: Calculate the energy involved in an asteroid impact Asteroid Characteristics: Spherical, iron-nickel with density of 7800 kg/m 3 Diameter 40 meters Velocity 20,000 meters/second

Energy equation for a moving object: KE = ½ mv 2 Kinetic Energy = KE Mass = m Velocity = v

What do we need to know to solve the problem? KE = ½ mv 2 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/m 3 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/m 3 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 X Volume = 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 cm 3

(1 a) Calculate Volume: Find the volume of the asteroid: Remember it is a spherical asteroid… V = (4/3) × pi × r 3 Use 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 × r 3 Radius = 20 m Pi = 3.14 So, 20 3 = 8,000 m 3 Volume = (4/3) x 3.14 x 8,000 m 3

Volume is…. 33,510 m 3 = (4/3) x 3.14 x 8,000 m 3

(1 b) Find the Total Mass Multiply the volume by density: Density = 7800 kg/m 3 (given) Volume = 33,510 m 3 (calculated) 33,510 m 3 x 7800 kg/m 3 =

(1 b) Total Mass is… 261,378,000 kg = 33,510 m 3 x 7800 kg/m 3

(1 c) Energy of the Asteroid KE = ½ mv 2 Mass = 261,378,000 kg (calculated) Velocity = 20,000 m/s (given) (20,000 m/s) 2 = 400,000,000 m/s 2

Time to plug in #’s again KE = ½ x 261,378,000 kg x 400,000,000 m/s 2

(1 c) The Energy is… KE = x Joules Joules are kg * m/s 2 Or about the energy needed to lift a quarter pound hamburger straight up one meter in one second