1
Question
What are collisions? Explain the possible types of collisions. Develop the theory of one dimensional elastic collision.
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Solution
1.Collision means two objects coming into contact with each other for a very short period. In other words, collision is a reciprocative interaction between two masses for a very short interval wherein the momentum and energy of the colliding masses changes. While playing carroms, you might have noticed the effect of a striker on coins when they both collide.
2.Types Of Collision:Generally, the law of conservation of momentum holds true in the collision of two masses but there may be some collisions in which Kinetic Energy is not conserved. Depending on energy conservation, conservation may be of two types:
A.Elastic Collision: In the elastic collision total momentum, the total energy and the total kinetic energy are conserved. However, the total mechanical energy is not converted into any other energy form as the forces involved in the short interaction are conserved in nature.B.Inelastic Collision: In the inelastic collision, the objects stick to each other or move in the same direction. The total kinetic energy in this form of collision is not conserved but the total momentum and energy are conserved. During this kind of collision, the energy is transformed into other energy forms like heat and light.
3.Inelastic One Dimensional CollisionIn inelastic one dimensional collision, the colliding masses stick together and move in the same direction at same speeds. The momentum is conserved and Kinetic energy is changed to different forms of energies. For inelastic collisions the equation for conservation of momentum is :m1u1+m2u2=(m1+m2)v
Since both the objects stick, we take final velocity after the collision asv. Now v shall be:
=m1u1+m2u2m1+m2
The kinetic energy lost during the phenomenon shall be:
E=12m1u22–12(m1+m2)v2
2.Types Of Collision:
Generally, the law of conservation of momentum holds true in the collision of two masses but there may be some collisions in which Kinetic Energy is not conserved. Depending on energy conservation, conservation may be of two types:
A.Elastic Collision: In the elastic collision total momentum, the total energy and the total kinetic energy are conserved. However, the total mechanical energy is not converted into any other energy form as the forces involved in the short interaction are conserved in nature.
B.Inelastic Collision: In the inelastic collision, the objects stick to each other or move in the same direction. The total kinetic energy in this form of collision is not conserved but the total momentum and energy are conserved. During this kind of collision, the energy is transformed into other energy forms like heat and light.
3.
Inelastic One Dimensional Collision
In inelastic one dimensional collision, the colliding masses stick together and move in the same direction at same speeds. The momentum is conserved and Kinetic energy is changed to different forms of energies. For inelastic collisions the equation for conservation of momentum is :
m1u1+m2u2=(m1+m2)v
Since both the objects stick, we take final velocity after the collision asv. Now v shall be:
=m1u1+m2u2m1+m2
The kinetic energy lost during the phenomenon shall be:
E=12m1u22–12(m1+m2)v2
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