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Elastic collision
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When two masses collide elastically in a one-dimensional displacement, they will move independently both before and after the collision.
In an elastic collision, both momentum and energy are conserved throughout the entire process.
ID:(1962, 0)
Elastic collision
Storyboard
When two masses collide elastically in a one-dimensional displacement, they will move independently both before and after the collision. In an elastic collision, both momentum and energy are conserved throughout the entire process.
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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, it is possible to represent the elastic collision between the mass 1 ($m_1$) and the mass 2 ($m_2$) using a positiontime diagram. In this graph, the horizontal axis represents time, while the vertical axis represents position:
The fact that the collision is elastic means that no energy is lost. As a result, both masses continue moving independently after the impact. Therefore, it is necessary to consider two velocities for each mass: the initial velocities the speed of the first object before collision ($v_1$) and the speed of the second object before the collision ($v_2$), and the final velocities after the collision the speed of the first object after the collision ($u_1$) and the speed of the second object after the collision ($u_2$).
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 in a one-dimensional system, the sum of their linear momenta before the collision is equal to the sum of their linear momenta after the collision. Therefore, if the velocities before the collision are the speed of the first object before collision ($v_1$) and the speed of the second object before the collision ($v_2$), and the velocities after the collision are the speed of the first object after the collision ($u_1$) and the speed of the second object after the collision ($u_2$), it holds that:
When two objects with masses the mass 1 ($m_1$) and the mass 2 ($m_2$) collide in a one-dimensional system, the sum of their kinetic energies is conserved before and after the collision. Before the collision, the kinetic energies are associated with the velocities the speed of the first object before collision ($v_1$) and the speed of the second object before the collision ($v_2$) of the objects. After the collision, the kinetic energies correspond to the final velocities the speed of the first object after the collision ($u_1$) and the speed of the second object after the collision ($u_2$) of each object.
This conservation of kinetic energy is mathematically expressed as:
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:(1962, 0)