A) CONTEXT
Izuku Midoriya tries to drag a pickup truck along the beach, in volume 1 and chapter 2 failing but later you can see how he has managed to move it to pile it up with the rest of the trash at the end on the last day of training. Being a quirkless after training with All Might.
B) THEORETICAL APPROACH
Izuku Midoriya is able at the end of the training to not only move the pickup truck but also to lift it up to the top of the waste pile clearly without using the wheels of the pickup truck because there is no route available to do so. Therefore, we have a situation in which the sum of the forces acting on the pickup truck vertically plus those acting on the boy must be less than the force that the boy is able to exert, otherwise he would simply stay in place with the truck on top of him without being able to move, let alone lift it up there.
C) ASSUMPTIONS
- Planet Earth is a sphere of radius R that rotates about its own axis uniformly.
- The mass beyond radius R is abysmally less than the total mass of the planet.
- The density of air is constant over the entire height from the ground to the top of the debris pile.
- The density of the air is that at 393 K and 101,325 Pa.
- The volume and density of both Izuku and the pick up truck are assumed constant.
- The pickup truck unloaded with waste is lifted in its entirety by Izuku.
- The gravitational and electromagnetic forces of other celestial bodies are ignored.
- Neither Izuku, nor the pickup truck, nor the Earth possess electric charge.
- The height of the center of mass of the Izuku and pickup truck assembly is abysmally less than R.
- 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.
- The dimensions of the pickup truck are: Height (Between 1.29 and 2.00 m), width (Between 1.26 and 5.95 m) and depth (Between 2.55 and 7.50 m).
- The volume of the pickup truck is assumed to be a 3D rectangle.
- The density of a human body is between 900 kg/m³ (100% fat) and 1,100 kg/m³ (100% muscle).
- The mass of a pickup truck is between 2,250 and 3,150 kg.
D) DEVELOPMENT
1) Izuku force
The Izuku force will be greater than the total vertical force acting on the pickup truck and himself, we are then left with this formula:
Where:
Fi: Izuku's Strength.
Ft: Total Force on the Izuku and Truck system.
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2) Total Force
If we know that the Total Force required has direction perpendicular to the ground, opposite direction to the sum of forces and modulus (Value) equal to the sum of these forces... And furthermore, we take into account that the system of bodies are in a gravitational field that pushes them towards the ground, that the bodies are rotating next to the planet where they rest that 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 resulting forces are parallel to each other and perpendicular to the ground that all the forces are aligned giving us the following formula:
Where:
Ft: Total Force on the Izuku and pickup truck system.
Fg: Gravitational Force (by gravitational field).
Fe: Thrust Force (by fluid displacement).
Fc: Centrifugal Force (By the rotation around the Earth's spin axis).
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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 ( By gravitational field ).
m: Total mass (Izuku mass plus truck mass) = 2,800 ± 500 kg.
g: Earth's 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 Izuku ≈ 60 ± 5 kg
m''': Mass pickup truck ≈ 2,700 ± 500 kg
R: Radius of the Earth = 6,370,000 ± 10,000 m
RESULT: Fg ≈ 27,000 ± 5,000 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': Density of air (393 K and 101,325 Pa) = 1.2 ± 0.1 kg / m³.
V: Total Volume (Izuku Volume plus pickup truck volume) = 40 ± 25 m³
g: Earth's Gravity (Sea Level) = 9.820 ± 0.027 m/s².
V'': Izuku's volume ≈ 0.06 ± 0.008 m³.
V''': Pickup truck's volume ≈ 40 ± 25 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 Izuku ≈ 60 ± 5 kg
m''': Mass pickup truck ≈ 2,700 ± 500 kg
𝞺'': Density of Izuku ≈ 1,000 ± 100 kg / m³.
𝞺''': Density of the pickup truck ≈ 68 ± 40 kg / m³.
RESULT: Fe ≈ 500 ± 300 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 obtaing 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 ( Izuku mass plus pick up mass ) = 2.800 ± 500 kg
m'': Izuku mass = 60 ± 5 kg
m''': Pickup truck mass ≈ 2,700 ± 500 kg
T: Earth's Rotation Period = 86.400 s
RESULT: Fe ≈ 94 ± 17 N
E) RESULTS
Fg ≈ 27,000 ± 5,000 N
Fe ≈ 500 ± 300 N
Fc ≈ 94 ± 17 N
Ft ≈ Fg - Fe - Fc ≈ 26,000 ± 5,000 N
RESULTS: Fi ≤ Fr ≈ 26,000 ± 5,000 N
Izuku Midoriya is expected to realize a force greater than 21,000 N.
E) IMPROVEMENT
1) The pre-entry value is in the input:
Izuku Pre-Training All Might Quirkless
Having these values:
Fi' ≤ 1,200 ± 400 N
Fi'' ≥ 26,000 ± 5,000 N
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2) The improvement in strength training will be greater than or equal to the division of both measures:
Where:
M = Strength Training Improvement.
Fi' = Izuku strength before training.
Fi'' = Izuku strength after training.
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3) Making calculations:
M ≥ Fi'' : Fi' = 22 ± 8 times
We therefore expect the improvement in strength to have been greater than at least 14 times.
