Brad,
Using your cartoon example sticking in numbers:
Forces needed to overcome breakaway friction (stiction) = C = 6 Newtons.
Man pushes with force B = 6N.
Ground exerts force on man D = 6N.
Car exerts force on man A = 6N.
No motion. All forces equal and opposite. Equilibrium.
All of a sudden, man increases to 9N. Now B' = 9N.
And D' = 9N. B' = D', equal and opposite.
Car pushes back on man with 9N, A'.
Now equilibrium is breached and C no longer applies due to motion. To balance equal and opposite force equation,
A' = C' + W + F = 9N where:
C' = rolling friction = 5N
W = windage = O
F = m × a = 4N.
A bit later,
C' = rolling friction = 5N
W = windage = 1N
F = m × a = 3N.
As speed increases, W increases from 1 to 4N, at which time equilibrium is again obtained and F = 0 and a = O. Again equal and opposite forces as there were at each instant during the dynamic period.
bi
*Flat surface assumed and windage is same as aerodynamic drag force.
Maybe chatGPT can explain it better than me-->
Newton's Second Law of Motion: According to Newton's second law, 𝐹=𝑚𝑎. F=ma, where F is the net force applied to an object, m is the mass of the object, and a is its acceleration. For the car to accelerate, there must be a net force acting on it in the direction of acceleration.
Resistive Forces: The car experiences several resistive forces that oppose its motion:
Friction: The force between the car's tires and the ground.
Air Resistance: The force of air pushing against the car as it moves.
Mechanical Resistance: Any internal resistance in the car's components, such as in the bearings or drivetrain.
Net Force: The net force on the car is the difference between the force applied by the man and the sum of all resistive forces. Mathematically, it can be expressed as :𝐹 net=𝐹 applied−𝐹 resistive. F
resistive is the total of all opposing forces
Acceleration: For the car to accelerate, 𝐹 net must be greater than zero.
If the applied force is greater than the resistive forces, the car will experience a net force in the direction of the push, resulting in acceleration.
Therefore, the man must push with a force that exceeds the total resistive forces in order for the car to accelerate. If his force is equal to the resistive forces, the car will move at a constant speed (assuming it was already in motion). If his force is less than the resistive forces, the car will either remain stationary or decelerate if it was initially moving.
So, as i stated, the applied force must be greater than the opposing force, in order for the car to accelerate.
This imbalance of force over distance (work done), is converted into the stored kinetic energy within the car.
So, when a mass is being accelerated, the forces are opposite, but they are not equal.
Brad
Never let your schooling get in the way of your education.