We can expand with the subscript o for original Whether it is elastic or perfectly elastic, we can model the transfer of momentum in a collision based on the above analysis. ![]() Where the subscript f denotes final or after the collision. If the original velocity of both pieces in the explosion is zero, then our equation becomes So in the case of an explosion, although the two objects will have equal and opposite momentum, their velocities will be proportional to the masses. Now using our definition of momentum we can say In turn, with the momentum-impulse relationship, we can say the change in momentum of object one is equal and opposite to the change of momentum of object 2Īnother way to look at this is we could say whatever momentum object 2 loses, object 1 gains. If we multiply both sides of this equation by this time, then we have impulse. This explosion lasts for a duration of time we will call Δt. Object 2 exerts an equal and opposite force back on object 1. With two objects exploding, object 1 exerts a force on object 2. Newton’s 3rd Law states that for every action there is an equal and opposite reaction. ![]() Let us begin by examining the case of a one-dimensional explosion. Oh, and yes, the plural of momentum is momenta. We might also think of the momentum of a system as the Net Momentum, or the sum of the momenta of all the parts. Although we might also say that Newton’s 3rd law results from the idea of Conservation of Momentum (as developed by Wallis). The origins of this idea can be found in Newton’s 3rd Law of Motion. You pushing the carts would be an external force. With two carts that collide, the magnets would be an internal force. In the example of two exploding carts, the spring would be an internal force. An external force is a force that is NOT part of the system, as opposed to an internal force. When we examine a system (which may two two objects, or multiple objects), the Law of Conservation of Momentum states that the momentum of a system is conserved IF there is no external force. We defined momentum as inertia in motion, or Conservation of Momentum and Newton’s 3rd Law I will return to this in a later posting. Both independently came up with calculus, but with very different notations. Leibniz developed the theory of Vis Viva looked at other conservation factors in collisions. However, there was a competing theory of collisions that persisted for hundreds of years called Vis Viva. Newton (and Descartes) based his work in refining the theory of Conservation of Momentum on the work of Wallis and Wren. There very well likely will be some deformation of the objects involved in the collision. In this process, there may be heat or sound generated. ![]() Inelastic Collision: Two objects when colliding stick together after the collision. Since they do touch, there is may be light, heat or sound generated, and there might be some deformation of the objects involved in the collision. Since they never touch, there is no light, heat or sound generated, and there is no deformation of the objects involved in the collision.Įlastic Collision (non-perfect): Two objects which when colliding bounce off of each and actually come into contact briefly. The force which repels them is a force that acts at a distance such as magnetism or the electric force. Perfectly Elastic Collision: Two objects which when colliding bounce off of each other and never actually touch. I would prefer to expand this into four categories:Įxplosions: Two objects which are stuck together fly apart due to an internal force (such as a spring, magnetism, chemical explosion, nuclear explosion, etc.) Wallis developed the theory for inelastic collisions and Wren developed the theory for elastic collisions. We might define an elastic collision as one in which the two colliding objects bounce off of each other, and an inelastic collision as one in which the two colliding objects stick together. Most textbooks will break collisions into two types, elastic and inelastic. Our current understanding of collisions traces its origins back to the studies of John Wallis and Christopher Wren (and upon who Newton based his work).
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