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Updated on 06th June, 2023 , 6 min read
When two objects collide, their kinetic energy is transferred between them, resulting in changes in their motion. An elastic collision is a type of collision in which there is no net loss of kinetic energy, and both momentum and energy are conserved. In this article, we will discuss the basics of elastic collisions, their characteristics, equations, and real-world applications.
An elastic collision is a type of collision in which the kinetic energy of the system is conserved. This means that the total kinetic energy of the system before the collision is equal to the total kinetic energy after the collision. In elastic collisions, the colliding objects bounce off each other without any deformation or loss of energy.
Elastic collisions have the following characteristics:
The Elastic Collision formula of momentum is given by:
m1u1 + m2u2 = m1v1 + m2v2
Where,
The Elastic Collision formula of kinetic energy is given by:
(1/2) m1u12 + (1/2) m2u22 = (1/2) m1v12 + (1/2) m2v22
One common example of an elastic collision is a game of billiards. When the cue ball strikes another ball, the collision between the two is almost perfectly elastic. This means that the kinetic energy of the cue ball is transferred to the second ball without any loss of energy. The second ball then moves away from the cue ball with the same speed and direction as the cue ball had before the collision.
Another example of an elastic collision is two molecules colliding in a gas. In this case, the kinetic energy and momentum of the two molecules are conserved, and they bounce off each other without any loss of energy. Elastic collisions between gas molecules are responsible for the transfer of heat and energy in a gas.
In both of these examples, the colliding objects bounce off each other without any deformation or loss of energy. This is a characteristic of elastic collisions, and it demonstrates the conservation of kinetic energy and momentum in these types of collisions.
Two billiard balls collide. Ball 1 moves with a velocity of 6 m/s, and ball 2 is at rest. After the collision, ball 1 comes to a complete stop. What is the velocity of ball 2 after the collision? Is this collision elastic or inelastic? The mass of each ball is 0.20 kg.
Solution:
To find the velocity of ball 2, use a momentum table.
Objects |
Momentum Before |
Momentum After |
Ball 1 |
0.20 kg × 6 m/s = 1.2 |
0 |
Ball 2 |
0 |
0.20 kg × v2 |
Total |
1.2 kg × m/s |
0.20 kg × v2 |
1.2 kg × m/s = 0.20 kg × v2
v2 =1.2 / 0.20 = 6 m/s
To determine whether the collision is elastic or inelastic, calculate the total kinetic energy of the system both before and after the collision.
Objects |
KE Before (J) |
KE After (J) |
Ball 1 |
0.50 × 0.20 × 62 = 3.6 |
0 |
Ball 2 |
0 |
0.50 × 0.20 × 62 = 3.6 |
Total |
3.6 |
3.6 |
Since the kinetic energy before the collision equals the kinetic energy after the collision (kinetic energy is conserved), this is an elastic collision.
The conservation of kinetic energy principle can be expressed mathematically as follows:
m1v1i + m2v2i = m1v1f + m2v2f
Where,
m1 and m2 are the masses of the colliding objects, v1i and v2i are their initial velocities, and v1f and v2f are their final velocities. This equation states that the sum of the initial kinetic energies of the two objects (m1v1i^2/2 + m2v2i^2/2) is equal to the sum of their final kinetic energies (m1v1f^2/2 + m2v2f^2/2).
The principle of conservation of momentum is also applicable to elastic collisions. According to this principle, the total momentum of the system before and after the collision is also conserved. Mathematically, this can be expressed as:
m1v1i + m2v2i = m1v1f + m2v2f
Where,
p1i = m1v1i and p2i = m2v2i are the initial momenta of the two objects, and p1f = m1v1f and p2f = m2v2f are their final momenta.
By combining the conservation of kinetic energy and the conservation of momentum principles, we can solve for the final velocities of the objects after the collision. This leads to the following equations:
v1f = (m1 - m2)/(m1 + m2) * v1i + (2m2)/(m1 + m2) * v2i
v2f = (m2 - m1)/(m1 + m2) * v2i + (2m1)/(m1 + m2) * v1i
These equations show how the final velocities of the two objects depend on their initial velocities and masses.
Elastic Collision |
Inelastic Collision |
The total kinetic energy is conserved. |
The total kinetic energy of the bodies at the beginning and the end of the collision is different. |
Momentum is conserved. |
Momentum is conserved. |
No conversion of energy takes place. |
Kinetic energy is changed into other energy such as sound or heat energy. |
Highly unlikely in the real world as there is almost always a change in energy. |
This is the normal form of collision in the real world. |
An example of this can be swinging balls or a spacecraft flying near a planet but not getting affected by its gravity in the end. |
An example of an inelastic collision can be the collision of two cars. |
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By - Nikita Parmar 2024-09-06 10:59:22 , 6 min readAn elastic collision is a type of collision in which there is no net loss of kinetic energy, and both momentum and energy are conserved. In an elastic collision, the colliding objects bounce off each other without any deformation or loss of energy.
The main difference between elastic and inelastic collisions is that elastic collisions involve no loss of kinetic energy, while inelastic collisions involve a loss of kinetic energy due to deformation or friction. In an elastic collision, the colliding objects bounce off each other without any deformation or loss of energy. In an inelastic collision, the colliding objects stick together or deform upon collision, resulting in a loss of energy.
Some examples of elastic collisions in the real world include a game of billiards, the collision between gas molecules, and the docking of spacecraft.
The velocity of objects after an elastic collision can be calculated using the equations for conservation of momentum and kinetic energy. These equations can be used to determine the final velocities of the objects after the collision.
Yes, kinetic energy is conserved in an elastic collision. This means that the total kinetic energy of the system before the collision is equal to the total kinetic energy after the collision.
A perfectly elastic collision is a special type of elastic collision in which the colliding objects not only bounce off each other without any deformation or loss of energy but also have the same velocity after the collision as they did before the collision. In other words, in a perfectly elastic collision, the colliding objects bounce off each other without any loss of kinetic energy and without any change in their velocities.
In an elastic collision, the motion of the colliding objects is affected by the conservation of momentum and energy. The colliding objects bounce off each other without any deformation or loss of energy, and their final velocities depend on their masses and initial velocities.
The coefficient of restitution is a value that represents the elasticity of a collision. It is defined as the ratio of the relative velocity of separation to the relative velocity of approach. In an elastic collision, the coefficient of restitution is equal to 1.
Yes, a collision can be partially elastic. In a partially elastic collision, some of the kinetic energy is conserved, but some is lost due to deformation or friction.