# The chapter begins with a mention of the issue of energy conservation discussed in chapter six

﻿Chapter 7

The chapter begins with a mention of the issue of energy conservation discussed in chapter six. The concept of energy conservation is used to introduce the concept of the conservation of linear momentum, electric charge as well as angular momentum. The chapter therefore focuses on how linear momentum is conserved as well as how Newton’s law can be reformulated to form the law of conservation of momentum. This law is then applied in the analysis of collisions, where two or more objects interact. In addition, the internal mechanics of objects which are in motion have also been focused on in chapter 7, with the chapter concluding with an introduction of center of mass.

The definition of the linear momentum of an object is provided as the product of its mass (m) and its velocity (v). P=mv, with the direction of the velocity and momentum being the same. The concept of higher velocity resulting in higher momentum is also explored at the beginning of the chapter. The relationship between momentum and force is also introduced, with the change in momentum be it an increase, decrease, or change of direction, coming about as a result of the additional net force applied. ∑F = Δp/Δt, which can further be reworked to mean ∑F = m(Δv/Δt), which is more convenient when calculating F for objects that lose mass while in motion.

The next part of the chapter focuses on conservation of momentum, arguing that in cases of a collision which results in a change of momentum for the two objects, the sum of their momenta will remain the same as before the collision mAvA+mBvB=(mAvA)1+(mBvB)1. This means that the total vector momentum stays constant and is therefore conserved. The equation can be reworked further using Newtion’s 2nd and 3rd laws to be ΔPA=FABΔt. Further based on Newton’s second law, the net force on an object in the case of a collision is usually equal to its momentum change as already mentioned F=Δp/Δt. This equation is then related to impulse, which is calculated as FΔt, after Δt is multiplied on both sides of the equation, this therefore means that the change in momentum is equal to impulse (Δp which is also equal to mΔv).

The chapter also explores the relationship between conservation of energy as well as momentum when it comes to collisions, and how the conservation laws of momentum can be used to explore the motion of objects after collision. For instance the chapter argues that the absence of heat or any other form of energy after collision, means that kinetic energy is conserved, with collisions in which the total kinetic energy is conserved being referred to as elastic collisions, for which 1/2mAv2A +1/2mBv2B= 1/2mA v’2A + 1/2mBv’2B

In cases where the kinetic energy is not conserved, the collisions are referred to as inelastic collisions, although the total energy is still conserved as the kinetic energy is changed into other forms of energy; the total energy will therefore be the sum of the kinetic energy and the other energy forms with the above equations applying to one dimension collisions (Collisions in which the vector is similar). In three or two dimension collisions, the projectiles of the objects colliding must be taken into account and as such based on figure 7-19, the XY plane and the resultant angles are used, such that:

MAvA = mAv’A CosΘ’A +mBv’BCosΘ’B in cases where Px is conserved or

0=mAv’ASinΘ’A+mBv’BSinΘ’B in cases wher Py is conserved