Maya Ellison
A perfectly plastic collision, also known as a perfectly inelastic collision, occurs when two objects collide and stick together, moving as a single object. This type of collision results in the maximum loss of kinetic energy, often due to internal friction, and is characterised by a coefficient of restitution of zero. In a perfectly inelastic collision, momentum is conserved, but kinetic energy is not. This is in contrast to an elastic collision, where kinetic energy is conserved and the objects involved do not stick together. Examples of perfectly inelastic collisions include a wet mud ball thrown against a wall and a ballistic pendulum, where a projectile embeds itself into a target.
| Characteristics | Values |
|---|---|
| Coefficient of restitution | 0 |
| Kinetic energy conserved | No |
| Momentum conserved | Yes |
| Objects stick together | Yes |
| Objects move as a single object | Yes |
| Total kinetic energy | Lost |
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What You'll Learn
Kinetic energy is lost in inelastic collisions
A perfectly inelastic collision occurs when the maximum amount of kinetic energy in a system is lost. In such a collision, the two particles stick together, bonding them together. This bonding energy usually results in a maximum kinetic energy loss in the system.
In a perfectly inelastic collision, the internal energy of the colliding masses increases. Energy is conserved, but kinetic energy is not conserved; the increase in internal energy must be accounted for. For example, the colliding masses can change shape and increase in temperature. The objects might deform, and energy is then trapped in the stresses and strains of the deformed material.
Even in a vacuum, the inelastic deformation would result in an increase in the temperatures of the blocks. An increase in temperature means there is an increase in the kinetic energy of the atoms and molecules of the blocks, i.e., an increase in kinetic energy at the microscopic level. The lost macroscopic kinetic energy associated with the overall motion of the blocks is converted to microscopic kinetic energy.
In the real world, partially inelastic collisions are the most common form of collisions. In this type of collision, the objects involved do not stick together, but some kinetic energy is still lost. This kinetic energy can be lost through friction, sound, and heat. The sound heard from a collision represents a substantial amount of energy, as it radiates out in all directions.
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Objects stick together after a perfectly inelastic collision
When objects collide, they can either stick together or bounce off one another. A perfectly inelastic collision occurs when the maximum amount of kinetic energy in a system is lost, and the colliding particles stick together. This phenomenon is also known as a plastic collision. In such a collision, kinetic energy is lost by bonding the two bodies together, and this bonding energy usually results in a maximum kinetic energy loss of the system.
In a perfectly inelastic collision, the objects involved do not separate but move together at the same speed. This is because the momentum of the system is conserved, while kinetic energy is not. For example, if two objects of equal mass initially head directly towards each other at the same speed and collide, they will stick together and come to a stop. This is different from a perfectly elastic collision, where the total kinetic energy of the two bodies remains the same, and the objects separate after impact.
The distinction between perfectly elastic and perfectly inelastic collisions can be understood through the coefficient of restitution. If the coefficient is 1, the collision is perfectly elastic, and if it is 0, the collision is perfectly inelastic. Partially inelastic collisions are the most common form of collisions in the real world, where some kinetic energy is lost, but the objects do not stick together.
Perfectly elastic collisions are not commonly observed in everyday life and are only possible with subatomic particles. On the other hand, perfectly inelastic collisions can be approximated by the interactions of objects such as billiard balls, although true perfectly inelastic collisions are idealized and do not fully occur in reality.
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Momentum is conserved in inelastic collisions
A perfectly plastic collision is a type of inelastic collision. Inelastic collisions occur when two objects collide and do not bounce apart but instead may stick together, resulting in a shared velocity after the collision. In such collisions, kinetic energy is lost but momentum is conserved. This is because some of the kinetic energy is transformed into other forms of energy, such as heat or sound.
The conservation of momentum is a fundamental principle in physics, known as the conservation of linear momentum. It holds true for all types of collisions, including perfectly plastic or inelastic collisions. This means that the total momentum before a collision is equal to the total momentum after the collision.
For example, when two cars collide and stick together, this is an inelastic collision. While the combined momentum of the cars remains the same, the total kinetic energy is less than before the collision due to energy lost as heat and deformation. This is also true in the case of a ball dropped on a surface, which bounces back at a lower height than it fell from, losing energy to deformation and heat.
In an inelastic collision, the momentum of the system remains conserved, but kinetic energy is not. This is because, in an inelastic collision, some kinetic energy is always lost. This loss of kinetic energy can occur through friction, sound, and heat. Partially inelastic collisions, where the objects involved do not stick but still experience kinetic energy loss, are the most common form of collisions in the real world.
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Internal friction causes kinetic energy loss
A perfectly inelastic collision, or plastic collision, occurs when the maximum amount of kinetic energy in a system is lost. In such a collision, the particles stick together and move as one body. This type of collision results in the maximum kinetic energy loss of the system.
Internal friction is a force that resists the motion of elements within a solid material as it undergoes deformation. It is one of several types of friction, including dry, fluid, lubricated, skin, and kinetic friction. Friction is a non-conservative force that affects the mechanical energy of a system. It does this by doing negative work against the direction of the displacement vector.
In the context of collisions, friction can cause kinetic energy loss. For example, in a sliding block experiment, the momentum of a two-body system is conserved only if the surface has zero friction. If there is friction, the momentum of the two bodies is transferred to the surface they are sliding upon. Similarly, if there is air resistance, the momentum of the bodies can be transferred to the air, resulting in a loss of kinetic energy.
Friction can also convert mechanical energy into heat. For example, when you rub your hands together, they become warm as your kinetic and frictional energy is converted into heat. This is an example of how friction can cause a loss of useful energy, as the heat generated is too little to be used for anything practical.
In summary, internal friction can cause kinetic energy loss in a perfectly plastic collision by resisting the motion of elements within the colliding particles and converting mechanical energy into heat or other forms of energy that are not useful for practical purposes.
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The coefficient of restitution is 0 for perfectly inelastic collisions
In physics, the coefficient of restitution (COR) is a measure of the elasticity of a collision between two bodies. It is a dimensionless parameter defined as the ratio of the relative velocity of separation after a two-body collision to the relative velocity of approach before the collision. The COR is denoted as 'e' and its values range between 0 and 1. When two objects collide, their speeds after the collision depend on the material they are made of. The nature of the colliding materials is represented by the COR.
A perfectly inelastic collision occurs when the maximum amount of kinetic energy of a system is lost. In such a collision, the colliding particles stick together, and kinetic energy is lost by bonding the two bodies together. This bonding energy results in a maximum kinetic energy loss of the system. In a perfectly inelastic collision, the difference in the velocities of the two objects after the collision is zero because the objects stick together. Therefore, the COR for a perfectly inelastic collision is e = 0.
For example, in Rutherford scattering, deep inelastic scattering of electrons by proton targets revealed that most incident electrons interact very little and pass straight through, with only a few bouncing back. This indicates that the charge in the proton is concentrated in small lumps, similar to Rutherford's discovery that positive charge in an atom is concentrated at the nucleus. However, in the case of the proton, the evidence suggested three distinct concentrations of charge (quarks) instead of one.
A collision between two bodies in which the bodies stick together after colliding and then move as one body is called a perfectly inelastic collision or plastic collision. In this type of interaction, the momentum of the system remains conserved, and the loss of kinetic energy is maximum.
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Frequently asked questions
A perfectly inelastic collision, also known as a plastic collision, is when the maximum amount of kinetic energy is lost and the colliding particles stick together.
In an inelastic collision, kinetic energy is lost but the colliding particles do not stick together. In a perfectly inelastic collision, the kinetic energy loss is maximum and the particles stick together.
A common example of a perfectly inelastic collision is the "ballistic pendulum", where a bullet is shot into a wooden block suspended by a rope. The bullet embeds itself into the block, causing it to swing like a pendulum.
The final velocity of objects after a perfectly inelastic collision is given by the equation:
> V = (M1*V1 + M2*V2) / (M1 + M2)
Where M1 and M2 are the masses of the objects, and V1 and V2 are their velocities before the collision.
