Investigation Activity 4
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
Kinetic Energy = KE
Mass = m
Velocity = v
2
mv
What do we need to know to solve the
problem?
KE = ½
2
mv
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 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 cm3
(1 a) Calculate Volume:
Find the volume of the asteroid:
Remember it is a spherical asteroid…
V = (4/3) × pi ×
Use pi = 3.14
3
r
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
3
m =
(4/3) x 3.14 x 8,000
3
m
(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
2
mv
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
Joules are kg
16
10
Joules
2
m/s
Or about the energy needed to lift a quarter
pound hamburger straight up one meter in one
second