A) CONTEXT
Izuku Midoriya tries to drag a refrigerator with All Might on it at the beach, in volume 1 and chapter 2. Being quirkless and without any training.
B) THEORETICAL APPROACH
Izuku Midoriya is unable to move All Might along with the refrigerator, therefore we find a situation in which the force of static friction is greater than the force exerted by the boy. Therefore, we can assure that the boy's strength is lower than said force.
C) ASSUMPTIONS
- Planet Earth is a sphere of radius R that rotates on its own axis uniformly.
- The mass beyond radius R is abysmally lower than the total mass of the planet.
- The density of the air is constant throughout the height of the refrigerator plus that of All Might.
- The density of air is that existing at 393 K and 101,325 Pa.
- The volume and density of both the refrigerator and All Might are assumed constant.
- The contact surface of the refrigerator is parallel to the sandy ground.
- The refrigerator with All Might on it does not move or slide across the sandy floor.
- The force generated by Izuku is parallel to the surface of the ground and the base of the refrigerator.
- The weight of the rope or elastic band to pull the refrigerator and All Might is negligible.
- Izuku does not move or slide on the sand when applying the force.
- The gravitational and electromagnetic forces of other celestial forces are ignored.
- Izuku does not move or slide on the sand when applying the force.
- The gravitational and electromagnetic forces of other celestial forces are ignored.
- The refrigerator does not have an electrical charge nor does the planet Earth.
- The height of the center of mass of the All Might and refrigerator set is abysmally lower than R.
- There are no drag forces from the sand or the wind since there is no relative speed.
- The height of the center of mass of the All Might and refrigerator set is abysmally lower than R.
- There are no drag forces from the sand or the wind since there is no relative speed.
- The angular velocity (w) is constant throughout the Earth's sphere and equivalent to that of the Equator.
- Electromagnetic and gravitational interactions between the bodies forming the system are neglected.
- Electromagnetic and gravitational interactions between the bodies forming the system are neglected.
- The dimensions of the American refrigerator are: Height (Between 1.75 and 2.00 m), width (Between 0.90 and 1.00 m) and depth (Between 0.70 and 0.80 m).
- The density of a human body is between 900 kg/m³ (100% fat) and 1,100 kg/m³ (100% muscle).
- The friction coefficient for sand is similar with similar materials, with a wide range between 0.25 and 0.5.
- The american refrigerator's mass has a value between 50 y 100 kg.
- The american refrigerator's mass has a value between 50 y 100 kg.
D) DEVELOPMENT
0) Izuku's Strength
Izuku's force will be less than or equal to the friction force since he cannot move the refrigerator with All Might, we are then left with this formula:
Where:
Fi: Izuku's Strenght.
Fr: Refrigerator plus All Might Friction Force.
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1) Friction Force.
We know that the Friction Force that exists when applying a force on a body that is in contact with another is defined as a force proportional to the Normal Force that acts on a body in a factor µ which is a dimensionless scalar (Real Number) called Coefficient of Friction which depends on the materials that are in contact, the topology of their contact surfaces (The shape of their surfaces), the state of relative motion of the bodies in contact (Whether they are in motion or are still with respect to each other) ... etc. The Friction Force will be parallel to the ground (Being perpendicular to the Normal Force, parallel to Izuku's Force and opposite to Izuku's Force). The equation of the Friction Force will be the following:
Where:
Fr: Friction Force.
µ: Static Friction Coefficient ≈ 0.38 ± 0.13
N: Normal Force.
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2) Normal Force
If we know that the Normal Force has a direction perpendicular to the contact surface, a direction opposite to the sum of forces and a module (Value) equal to the sum of these forces... And furthermore, we take into account that the bodies of the system are in a gravitational field that pushes them towards the ground, that the bodies are rotating with the planet where they rest which pushes them in the opposite direction to the ground and that the bodies occupy a volume within a fluid (air) which they displace and this volume of fluid in response exerts a force in the opposite direction to the ground, we can deduce that as all the resultant forces are parallel to each other and perpendicular to the contact surface that all the forces are aligned giving us the following formula:
Where:
N: Normal Force.
Fg: Gravitational Force (Due to gravitational field).
Fe: Thrust Force (Due to the displacement of fluid).
Fc: Centrifugal Force (Due to the rotation around the axis of rotation of the Earth).
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3) Gravitational Force
The Gravitational Force is the force with which one body attracts another according to its mass. It is defined as follows, according to Newton's Laws of Gravitation for our system:
Where:
Fg: Gravitational Force ( Due to gravitational field )
m: Total mass (All Might mass plus refrigerator mass) = 330 ± 25 kg
g: Earth Gravity (Sea Level) = 9.820 ± 0.027 m/s²
G: Universal Gravitational Constant = (6.6742 ± 0.0010) x 10^-11 N m² / kg²
M: Mass Planet Earth = ( 5.97 ± 0.01 ) x 10^24 kg
m'': Mass All Might = 255 ± 1 kg
m''': Mass refrigerator ≈ 75 ± 25 kg
R: Radius of the Earth = 6,370,000 ± 10,000 m
RESULT: Fg ≈ 3,240 ± 250 N
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4) Thrust Force
The Thrust Force is the force with which a fluid tries to expel from its interior a body that occupies a certain volume. It is defined as follows, according to Archimedes' Principle for our system:
Where:
Fe: Thrust force. (For being in the bosom of a fluid).
𝞺': Air density ( 393 K and 101,325 Pa) = 1.2 ± 0.1 kg / m³
V: Total Volume (All Might volume plus refrigerator volume) = 1.595 ± 0.15 m³
g: Earth Gravity (Sea Level) = 9.820 ± 0.027 m/s²
V': All Might Volume ≈ 0.255 ± 0.026 m³
V'': Refrigerator volume ≈ 1.34 ± 0.15 m³
G: Universal Gravitation Constant = (6.6742 ± 0.0010) x 10^-11 N m² / kg²
M: Mass Planet Earth = ( 5.97 ± 0.01 ) x 10^24 kg
R: Radius of the Earth = 6,370,000 ± 10,000 m
m'': Mass All Might = 255 ± 1 kg
m''': Refrigerator mass ≈ 75 ± 25 kg
𝞺'': Density of All Might ≈ 1,000 ± 100 kg / m³
𝞺''': Refrigerator density ≈ 60 ± 20 kg / m³
RESULT: Fe ≈ 18.8 ± 2.4 N
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5) Centrifugal Force
The centrifugal force is the force to which a body describing a circular motion is subjected, which has a tangential velocity that makes it move away from describing the circular motion and obteing freedom. This is defined as follows, according to Newton's Second Law for our system:
Where:
Fc: Centrifugal Force. (Because it is describing a circular rotation)
w: Angular Velocity = 7.27 x 10^-5 rad / s
r: Radius at the center of the circumference = 6,370,000 ± 10,000 m
R: Radius of the Earth = 6,370,000 ± 10,000 m
m: Total mass ( All Might mass plus refrigerator mass ) = 330 ± 25 kg
m'': Mass All Might = 255 ± 1 kg
m''': Refrigerator mass ≈ 75 ± 25 kg
T: Earth's Rotation Period = 86,400 s
RESULT: Fe ≈ 11.1 ± 0.8 N
E) Results
µ ≈ 0.38 ± 0.13
Fg ≈ 3,240 ± 250 N
Fe ≈ 18.8 ± 2.4 N
Fc ≈ 11.1 ± 0.8 N
N = Fg - Fe - Fc ≈ 3,210 ± 250 N
Fr = µ N ≈ 1,200 ± 400 N
RESULT: Fi ≤ Fr ≈ 1,200 ± 400 N
Izuku Midoriya is expected to perform less than 1,600 N force.
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