Certain Laws of Motion and Equilibrium

Whether at rest or moving, all material bodies have an inertial force that works to maintain them in their current state of motion.

This inertia is proportional to the amount of matter they contain.

Material bodies have 2 two properties:

1. Impenetrability
2. Inertia

These 2 are always opposed to one another in Nature, making laws necessary to bring them into harmony.*

When two bodies encounter one another, they cannot penetrate one another.

Therefore, the rest of one and the motion of the other (or the motion of both) must be changed.

This change depends on the force with which the two bodies collide.

We assume that the bodies collide directly:

1. Their centers of gravity move only along the straight line that connects them
2. The point of contact in the collision lies on this line
3. The tangent surfaces at the point of contact are penpendicular to this line.

This last condition is always true if the two bodies are solid spheres composed of a homogenous material, as we assume here.

If a body moves with a certain speed and encounters a second body at rest, the impact would be the same as if the second body, moving with the speed of the first, had collided with the first body at rest.

If two bodies move in opposite directions and collide, the impact would be the same as if one body were at rest and the second body moved with a speed equal to the sum of the original two speeds.

If two bodies move in the same direction and collide, the impact would be the same as if one body were at rest and the second body moved with a speed equal to the difference of the original two speeds.

Thus, whenever two bodies collide, the impact is generally the same as long as their relative speed (i.e., the sum or difference of their speeds) is the same, regardless of their individual speeds.

The magnitude of the impact depends only on the relative speed of the 2 colliding bodies.

This is proven by bodies being transported on an invisible, massless plane.

• The speed of Body 1 vanishes
• The speed of Body 2 has either the sum or the difference of the original 2 speeds.

The impact of the 2 bodies on the moving plane would be the same as on a stationary plane.

What are the effects of elasticity on the collision?

• In a perfectly inelastic body, the parts are inseparable and inflexible. Hence, its shape cannot be changed.
• In a perfectly elastic body, the parts may deform. But they always recover to their original shape and situation.

I do not know the origin of this elasticity. I only know its effects.

I will not discuss “squishy” or fluid bodies which are composed of inelastic or elastic bodies.

When 2 inelastic bodies collide, their parts are inseparable and inflexible.

• Hence, the impact can affect only their speed.

The 2 bodies press and push until the speed of Body 1 equals the speed of Body 2.

After the impact, inelastic bodies move with a common speed.

However, when 2 elastic bodies collide the impact deforms their parts.

The two bodies do not remain touching each other.

The restoration of their former shape causes them to rebound from one another, separating from one another at the same speed with which they approached.

Their relative speed was the sole cause of their initial collision.

The rebounding should produce an effect equal to that which caused the collision.

Thus, the final relative speed of the 2 bodies should equal the initial relative speed, albeit with opposite direction.

Hence, the final relative speed of 2 elastic bodies after the collision should be the same as the initial relative speed.