Force

Newton's equation F=ma is the formula that shows that gravity depends only on mass. It is not an equation for a force exerted by a mass in motion (kinetic energy). Imagine 1kg ball, and 2kg ball falling from 100m. Different masses will fall with the same uniform acceleration 10 m/s2. The air resistance takes about 0.2 m/s2, but I will say 9.8 m/s2 because everybody says so… If a=F/m, then for the acceleration to remain constant, which it does, the force acting on the mass must be directly proportional to the mass! If a=F/m, then to keep the "a" value at constant 9.8 m/s2 the force "F" has to be F=9.8 and F=19.6. The force acting on a mass depends only on its mass. The bigger the mass, the bigger the gravity acting on it. It means that gravity is equal to mass. Hence, the force of gravity FG=am. The force of gravity is potential energy (PE) of a mass, which is the mass itself. A brick falling from 1-st floor doesn’t exert the same force like the same brick falling from 10-th floor. It has been assumed that, if an accelerating mass is falling, the force must be its acceleration times mass. It is only true for the force acting on the mass, which is gravity, not the force exerted by the mass. Of course to avoid confusion from such screwed ups the words like “momentum” “kinetic energy” “impact” are used as if they really meant something different. True, they pick on different aspect, but they do have to have the same value because of conservation of energy law and the fact that they all are cause by mass and velocity! If F=ma, then a car weighing 2000 kg traveling with uniform motion and hitting a pedestrian would not hurt him because according to this equation it would not exert any force, because the acceleration would be zero, F =2000*0 =0! If the car were decelerating (slamming on brakes), the acceleration would have a negative value, or as you prefer it would not be there. Now (of course) it would be “impact” or “momentum”…

Now, what is the equation for the force exerted by a mass? It's F=mv.

The equation for force exerted by mass stays the same independent of the motion's history. It's the same for accelerated, decelerated, uniform or jerking motion! What matters is only at what velocity the kinetic energy of a mass was transferred into force, when it exerted it.

Work=force*distance

Newton's idea that work=force*distance is not logical. The definition of force as being “any influence producing a linear change in the momentum of a body” is wrong too. You can apply force to a stone and still not perform any work because of inertia. However, you did exert force. Exertion of force on an object does not depend on reaction of the object. That’s WORK! Work is the result of the force that you applied, not the force applied! Therefore you cannot use force in such equation. The equation for work is W=mass*distance. W=md. The inertia of the object can be calculated by subtracting force from work. The amount of work depends on mass and distance of displacement. It does not depend on friction or even inertia because it does not mater how much force or energy you lost. It matters how much work you have done. For the same reason it doesn't matter how much inertia have you defeated. Newton's equation for work contains "v," for velocity at which the mass is displaced. The velocity has no influence on the amount of performed work, therefore there is no place for it in such equation. To illustrate my point, imagine two workers who are going to move your furniture. One of them may do it in 2 hours, the other in 4 hours, but they still will perform the same work… The speed with which they will do work has nothing to do with the amount of work. It has to do with "power." It's easy to confuse "force" with "work" or "power" because not all their definitions in books are correct.

mc2

Einstein's equation for work W=-------------------- __ mc2

(1-v2/c2)0.5

may seem impressive but it contradicts Newton's equation W=0.5*mv2.

That means that at least one of them is wrong. When you analyze Einstein's equation it may strike you that it contains the speed of light squared "c2." The presence of the speed of light is just another "Mickey Mouse" factor. There is no logical relationship between the speed of light and performed work! If you push your car you performed work but what the speed of light has to do with the amount of work you did? Surprise! Surprise! Nothing! Using the speed of light in the equation for work is just as silly as using the speed of sound or the speed of Wilde Coyote.

PAWEL KOLASA