One-dimensional collision between body A and body B
Let’s look at the figure above: it shows us a case of one-dimensional collision between two bodies A and B, of mass m A in B , which separate after the collision. Let’s suppose that the values of m A , m B , v A and v B are known and that we want to determine the values of v’ A and v’ B . The first step is to consider the conservation of the momentum of the system:
Because the equation has two unknowns, the data are not enough to solve the one-dimensional collision problem. Isaac Newton, however, discovered, through his experiments, a relationship between the speeds of bodies before and after the collision. His relationship was as follows:
Newton called the letter e the coefficient of restitution . Therefore, in the above equation, the difference v’ A – v’ B is the velocity of A with respect to B after the collision, and the difference v A – v B is the velocity of A with respect to B before the collision. However, these differences will have opposite signs, because before the collision the bodies approach and after the collision the bodies move away. In this way, we have:
And so the minus sign in the above equation is placed for e terms > 0.