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Inelastic collision
Storyboard 
When two masses collide inelastically in a one-dimensional displacement, they will remain attached after the collision.
In an inelastic collision, energy is not fully conserved, meaning that a portion of the energy is transformed into deformation or heat.
ID:(1963, 0)
Inelastic collision
Storyboard
When two masses collide inelastically in one-dimensional motion, they will move together after the impact. In an inelastic collision, momentum is conserved, while part of the energy is absorbed, converting into deformations or heat within the combined bodies.
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To determine the center of mass of two particles, a calculation is performed based on the positions of both masses, the position of the first object ($x_1$) and the position of the second object ($x_2$), as well as their respective masses, the mass 1 ($m_1$) and the mass 2 ($m_2$), using the following equation:
From this calculation, it is possible to derive an expression for the velocity of the center of mass, the velocity of the center of mass of the particles ($v_{CM}$), which depends on the individual velocities the speed of the first object before collision ($v_1$) and the speed of the second object before the collision ($v_2$):
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In the one-dimensional case, the inelastic collision between masses the mass 1 ($m_1$) and the mass 2 ($m_2$) can be represented in a positiontime diagram. In this graph, the horizontal axis represents time, while the vertical axis represents position:
The fact that the collision is inelastic means that energy is lost. As a result, both masses move together after the impact, behaving as a single system. Therefore, it is necessary to consider two velocities before the collision (the speed of the first object before collision ($v_1$) and the speed of the second object before the collision ($v_2$)) and a common velocity after the collision (the velocity of the center of mass of the particles ($v_{CM}$)).
The center of mass of two particles is calculated by considering their positions, represented as the position of the first object ($x_1$) and the position of the second object ($x_2$), along with their respective masses, the mass 1 ($m_1$) and the mass 2 ($m_2$). This calculation corresponds to a weighted average of the positions, where the weights are determined by the masses, resulting in the position of the center of mass ($x_{CM}$):
When two objects with masses the mass 1 ($m_1$) and the mass 2 ($m_2$) collide inelastically in a one-dimensional system, the sum of their linear momenta before the collision is equal to the linear momentum of the combined mass after the collision. This is expressed in terms of the velocities the speed of the first object before collision ($v_1$), the speed of the second object before the collision ($v_2$) and the velocity of the joint object after the collision ($u$) as:
In the context of an inelastic collision, when the mass 1 ($m_1$) and the mass 2 ($m_2$), moving at velocities the speed of the first object before collision ($v_1$) and the speed of the second object before the collision ($v_2$) respectively, collide, they remain joined after the impact and continue moving with a combined velocity the velocity of the joint object after the collision ($u$). During this process, the initial kinetic energy of the individual masses is transformed into the kinetic energy of the combined mass the mass 1 ($m_1$) + The mass 2 ($m_2$), which is generally lower. This reduction in kinetic energy is due to energy being dissipated through plastic deformation and/or heat generation during the collision.
The amount of energy dissipated, the energy lost in inelastic collision ($\Delta E$), as heat or plastic deformation energy, is expressed as the difference between the initial kinetic energy of the individual masses and the final kinetic energy of the combined mass, as shown in the formula:
The velocity of the center of mass of the particles ($v_{CM}$) is determined as a weighted average of the speed of the first object before collision ($v_1$) and the speed of the second object before the collision ($v_2$), using the masses the mass 1 ($m_1$) and the mass 2 ($m_2$) as weights, by means of:
ID:(1963, 0)