What is the formula for elastic and inelastic collision?
The Correct Answer and Explanation is:
In physics, the formulas for elastic and inelastic collisions describe how momentum and kinetic energy are transferred between objects during impact. Here’s a breakdown of each type:
Elastic Collision:
In an elastic collision, both momentum and kinetic energy are conserved. This type of collision commonly occurs between objects like gas molecules that bounce off each other without deformation or energy loss to other forms.
The key formulas for an elastic collision between two objects, with masses ( m_1 ) and ( m_2 ) and initial velocities ( u_1 ) and ( u_2 ), are:
- Conservation of Momentum:
[
m_1 u_1 + m_2 u_2 = m_1 v_1 + m_2 v_2
] - Conservation of Kinetic Energy:
[
\frac{1}{2} m_1 u_1^2 + \frac{1}{2} m_2 u_2^2 = \frac{1}{2} m_1 v_1^2 + \frac{1}{2} m_2 v_2^2
]
Where:
- ( v_1 ) and ( v_2 ) are the final velocities of the objects after collision.
In cases where two objects collide elastically in one dimension, the final velocities can be calculated using:
[
v_1 = \frac{(m_1 – m_2)u_1 + 2m_2 u_2}{m_1 + m_2}
]
[
v_2 = \frac{(m_2 – m_1)u_2 + 2m_1 u_1}{m_1 + m_2}
]
Inelastic Collision:
In an inelastic collision, momentum is conserved, but kinetic energy is not fully conserved; some of it is transformed into other energy forms, such as sound, heat, or deformation energy. A completely inelastic collision is a scenario where colliding objects stick together.
For an inelastic collision, the conservation of momentum is expressed as:
[
m_1 u_1 + m_2 u_2 = (m_1 + m_2) v
]
Where ( v ) is the common final velocity of the combined mass after collision.
Explanation
Elastic collisions are characterized by the conservation of both momentum and kinetic energy, resulting in no energy loss. These are ideal, theoretical collisions often used to model atomic or molecular interactions where energy exchange within the system is perfectly efficient.
In contrast, inelastic collisions are more common in real-world scenarios, where the objects may lose kinetic energy due to sound, heat, or other forms of energy dissipation. In cases of completely inelastic collisions, the objects merge and move with a single, combined velocity afterward. Thus, while both types of collisions conserve momentum, the distinction lies in the treatment of kinetic energy—fully conserved in elastic but partially lost in inelastic collisions.