Michiru throws a baseball repeatedly with enough force to create small craters in concrete. A baseball is 73mm to 76mm in diameter (or 7.3cm to 7.6cm). First for the size of the crater...
16 pixels = 7.3cm
1 pixel = 7.3cm/16 = 0.45625cm
0.45625cm X 37 = 16.88125cm
16.88125cm/2 = 8.440625cm
0.45625cm X 49 = 22.35625cm
22.35625cm/2 = 11.178125cm
Then the width of the bottom of the crater...
186 pixels = 22.35625cm
1 pixel = 22.35625cm/186 = 0.120194892cm
0.120194892cm X 103 = 12.3800739cm
12.3800739cm/2 = 6.19003695cm (0.0619003695m)
Then the depth...
212 pixels = 7.3cm
1 pixel = 7.3cm/212 = 0.0344339623cm
0.0344339623cm X 111 = 3.82216982cm
Volume of the area broken as a conical frustrum.
V = (1/3)π(r^2+rR+R^2)h
= (1/3) X π X (6.19003695^2 + 6.19003695 X 8.440625 + 8.440625^2) X 3.82216982
= 647.649296cm^3
Violent fragmentation of cement is between 17 joules per cm^3 to 20 joules/cm^3.
E = 647.649296 X 17
= 11010.038 joules
That's a respectable amount of energy, but what we're really after is the speed, which we'll do using drag coefficient. For this, we need the energy of the impact, the distance the ball travelled and the surface area of the ball. The distance from a baseball mound to home base is 60 feet & 6 inches, or 18.4404m.
90 pixels = 18.4404m
1 pixel = 18.4404m/90 = 0.204893333m
0.204893333m X 143 = 29.2997466m
We'll need the surface area of the baseball.
A = 4πr^2
= 4 X π X 0.0365^2
= 0.0167415473m^2
Drag coefficient of a sphere is 0.5. Now to find our speed (using this calculator to find the square root).
DF = ½ρCAv2 X d
11010.038 X 2 = 0.5 X 0.0167415473 X 29.2997466
V^2 = 22020.076/0.245261547
V^2 = 89782.0154
V = 299.6364720790845m/s
Final Results
Michiru throws baseball (energy) = 11010.038 joules
Michiru throws baseball (speed) = 299.636m/s
1 pixel = 7.3cm/16 = 0.45625cm
0.45625cm X 37 = 16.88125cm
16.88125cm/2 = 8.440625cm
0.45625cm X 49 = 22.35625cm
22.35625cm/2 = 11.178125cm
Then the width of the bottom of the crater...
1 pixel = 22.35625cm/186 = 0.120194892cm
0.120194892cm X 103 = 12.3800739cm
12.3800739cm/2 = 6.19003695cm (0.0619003695m)
Then the depth...
1 pixel = 7.3cm/212 = 0.0344339623cm
0.0344339623cm X 111 = 3.82216982cm
Volume of the area broken as a conical frustrum.
V = (1/3)π(r^2+rR+R^2)h
= (1/3) X π X (6.19003695^2 + 6.19003695 X 8.440625 + 8.440625^2) X 3.82216982
= 647.649296cm^3
Violent fragmentation of cement is between 17 joules per cm^3 to 20 joules/cm^3.
E = 647.649296 X 17
= 11010.038 joules
That's a respectable amount of energy, but what we're really after is the speed, which we'll do using drag coefficient. For this, we need the energy of the impact, the distance the ball travelled and the surface area of the ball. The distance from a baseball mound to home base is 60 feet & 6 inches, or 18.4404m.
1 pixel = 18.4404m/90 = 0.204893333m
0.204893333m X 143 = 29.2997466m
We'll need the surface area of the baseball.
A = 4πr^2
= 4 X π X 0.0365^2
= 0.0167415473m^2
Drag coefficient of a sphere is 0.5. Now to find our speed (using this calculator to find the square root).
DF = ½ρCAv2 X d
11010.038 X 2 = 0.5 X 0.0167415473 X 29.2997466
V^2 = 22020.076/0.245261547
V^2 = 89782.0154
V = 299.6364720790845m/s
Final Results
Michiru throws baseball (energy) = 11010.038 joules
Michiru throws baseball (speed) = 299.636m/s
