Understanding conservation of energy using collision of elastic and inelastic bodies
Consider the impact between two bodies which move with different velocities along the same straight line. It is assumed that the point of impact lies on the line joining the centers of gravity of the two bodies. The behavior of these colliding bodies during the complete period of impact will depend upon the properties of the materials of which they are made. The material of the two bodies may be perfectly elastic or perfectly inelastic.
The bodies which rebound after impact are called elastic bodies and the bodies which does not rebound at all after its impact are called inelastic bodies. The impact between two lead spheres or two clay spheres is approximately an inelastic impact.
The loss of kinetic energy (EL) during impact of inelastic bodies is given by
![Loss of Kinetic Energy for elastic bodies Loss of Kinetic Energy for elastic bodies](data:image/png;base64,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)
where
m1 = Mass of the first body,
m2 = Mass of the second body,
u and u2 = Velocities of the first and second bodies respectively.
The loss of kinetic energy (EL) during impact of elastic bodies is given by
![Loss of Kinetic Energy for inelastic bodies Loss of Kinetic Energy for inelastic bodies](data:image/png;base64,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)
where
e = Coefficient of restitution.
![Coefficient of restitution Coefficient of restitution](data:image/png;base64,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)
Notes:
1. The relative velocity of two bodies after impact is always less than the relative velocity before impact.
2. The value of e=0, for perfectly inelastic bodies and e=1, for perfectly elastic bodies. In case the bodies are neither perfectly inelastic nor perfectly elastic, then the value of e lies between zero and one.
The bodies which rebound after impact are called elastic bodies and the bodies which does not rebound at all after its impact are called inelastic bodies. The impact between two lead spheres or two clay spheres is approximately an inelastic impact.
The loss of kinetic energy (EL) during impact of inelastic bodies is given by
where
m1 = Mass of the first body,
m2 = Mass of the second body,
u and u2 = Velocities of the first and second bodies respectively.
The loss of kinetic energy (EL) during impact of elastic bodies is given by
where
e = Coefficient of restitution.
Notes:
1. The relative velocity of two bodies after impact is always less than the relative velocity before impact.
2. The value of e=0, for perfectly inelastic bodies and e=1, for perfectly elastic bodies. In case the bodies are neither perfectly inelastic nor perfectly elastic, then the value of e lies between zero and one.
No comments:
Post a Comment