Inelastic Collision - Definition, Formula, Examples, FAQs

An inelastic collision refers to an event whereby two rigid bodies collide, and as a result, both of them lose a part of their kinetic energy – usually in the form of heat, sound or even changes to the deformation of the two colliding bodies. While these collisions cannot be referred to as elastic because kinetic energy before the collision and after the collision is not the same, momentum is still conserved. Inelastic collision examples can be observed in most daily activities: for instance, in a car crash, the vehicles deform inwards when they collide or when a ball of clay is thrown on the pavement and sticks. This is extremely important when discussing energy loss and how materials behave in practice.

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What is Collision?

A collision is a unique event where two or more bodies interact by getting in contact with each other for a short period of time, whereby they apply force on each other causing a change in their motion (velocity) or shape. In physics, the latter is an important subject since colliding bodies allow students to study the transfer and conservation of momentum and energy.

Collisions are classified based on how energy and momentum are conserved. They are,

• Elastic collision: Kinetic energy is conserved
• Inelastic collision: Kinetic energy is not conserved
• Completely inelastic collision: Kinetic energy is not conserved and the objects are attached after colliding.

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What is Inelastic Collision?

An inelastic collision is a collision in which there is a loss of kinetic energy. While the momentum of the system is conserved in an inelastic collision, kinetic energy is not. This is because some kinetic energy had been transferred to something else.

Inelastic collision examples:

• Two vehicles crashed.
• Clay ball when thrown against the wall.
• A vehicle hit the compound.

What is a Perfectly Inelastic Collision?

A perfectly inelastic collision is a special case of inelastic collision. In this scenario, the two objects stick together after the collision and move as a single unit. For instance, consider a wet ball of mud thrown against a wall - the mud ball sticks to the wall, exemplifying a perfectly inelastic collision.

The Formula for Inelastic Collision

When two objects collide inelastically, they move with a final velocity that can be calculated using the following formula:

$
V=\frac{\left(M_1 v_1+M_2 v_2\right)}{\left(M_1+M_2\right)}
$
Where,
$\mathrm{V}=$ Final velocity
$\mathrm{M}_1=$ Mass of the first object in kgs
$\mathrm{M}_2=$ Mass of the second object in kgs
$\mathrm{V}_1=$ Initial velocity of the first object in $\mathrm{m} / \mathrm{s}$
$\mathrm{V}_2=$ Initial velocity of the second object in $\mathrm{m} / \mathrm{s}$

Inelastic Collision in Two Dimensions

In a two-dimensional inelastic collision, the conservation of momentum is applied separately along each axis. This is because momentum is a vector equation, and there is a separate conservation of momentum equation for each dimension. However, there is only one conservation of energy equation.

Kinetic Energy in Inelastic Collision

In inelastic collisions, kinetic energy isn't conserved. The lost energy is often due to internal friction, which can cause the atoms to vibrate (creating heat) and deform the bodies involved.

Loss of kinetic energy in an inelastic collision

Consider $m_1$ and $m_2$ to be the masses of the two colliding objects. The object with mass $m_1$ moves with velocity $v_1$ and the object with mass $m_2$ is at rest position.

After the collision, the momentum of the objects is conserved. But, the two objects stick to each other. Hence, the kinetic energy is not conserved.

Kinetic energy, $\mathrm{E}=\mathrm{mv}^2 / 2$
The kinetic energy of the object $m_1$ before the collision, $\mathrm{E}_{\mathrm{i}}=\mathrm{m}_1 \mathrm{v}_1{ }^{2 / 2}$
Kinetic energy after the collision is, $E_{\mathrm{f}}=\left(m_1+m_2\right) v_{\mathrm{f}}^2 / 2$
Therefore, the loss of kinetic energy is given by,

$
(E i-E f) / E i=1-\frac{m_1+m_2}{m_1}\left(\frac{v_f^2}{v_i^2}\right)
$

Elastic Collision

Any collision in which the collided objects get separated after the collision is known as an elastic collision. In the case of elastic collision, kinetic energy gets conserved. One must use both conservation of momentum and conservation of energy to find the motions of the objects later.

Difference Between Elastic Collision and Inelastic Collision