Define momentum of a body prove that with the help of third law that total momentum of two bodies is concerved during collision provided no external force acts
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Consider two interacting objects. If object 1 pushes on object 2 with a force F = 10 N for 2 s to the right, then the momentum of object 2 changes by 20 Ns = 20 kgm/s to the right. By Newton's third law object 2 pushes on object 1 with a force F = 10 N for 2 s to the left. The momentum of object 1 changes by 20 Ns = 20 kgm/s to the left. The total momentum of both objects does not change. For this reason we say that the total momentum of the objects is conserved.
Newton's third law implies that the total momentum of a system of interacting objects that are not acted on by outside forces is conserved.
The total momentum in the universe is conserved. The momentum of a single object, however, changes when a net force acts on the object for a finite time interval. Conversely, if no net force acts on an object, its momentum is constant. For a system of objects, a component of the momentum along a chosen direction is constant, if no net outside force with a component in this chosen direction acts on the system.
Collisions
In collisions between two isolated objects Newton's third law implies that momentum is always conserved. In collisions, it is assumed that the colliding objects interact for such a short time, that the impulse due to external forces is negligible. Thus the total momentum of the system just before the collision is the same as the total momentum just after the collision. Collisions in which the kinetic energy is also conserved, i.e. in which the kinetic energy just after the collision equals the kinetic energy just before the collision, are called elastic collision. In these collisions no ordered energy is converted into thermal energy. Collisions in which the kinetic energy is not conserved, i.e. in which some ordered energy is converted into internal energy, are called inelastic collisions. If the two objects stick together after the collision and move with a common velocityvf, then the collision is said to be perfectly inelastic.
Note: In collisions between two isolated objects momentum is always conserved. Kinetic energy is only conserved in elastic collisions.
We always have m1v1i + m2v2i = m1v1f + m2v2f.
Only for elastic collisions do we also have (1/2)m1v1i2 + (1/2)m2v2i2 = (1/2)m1v1f2 + (1/2)m2v2f2.
Newton's third law implies that the total momentum of a system of interacting objects that are not acted on by outside forces is conserved.
The total momentum in the universe is conserved. The momentum of a single object, however, changes when a net force acts on the object for a finite time interval. Conversely, if no net force acts on an object, its momentum is constant. For a system of objects, a component of the momentum along a chosen direction is constant, if no net outside force with a component in this chosen direction acts on the system.
Collisions
In collisions between two isolated objects Newton's third law implies that momentum is always conserved. In collisions, it is assumed that the colliding objects interact for such a short time, that the impulse due to external forces is negligible. Thus the total momentum of the system just before the collision is the same as the total momentum just after the collision. Collisions in which the kinetic energy is also conserved, i.e. in which the kinetic energy just after the collision equals the kinetic energy just before the collision, are called elastic collision. In these collisions no ordered energy is converted into thermal energy. Collisions in which the kinetic energy is not conserved, i.e. in which some ordered energy is converted into internal energy, are called inelastic collisions. If the two objects stick together after the collision and move with a common velocityvf, then the collision is said to be perfectly inelastic.
Note: In collisions between two isolated objects momentum is always conserved. Kinetic energy is only conserved in elastic collisions.
We always have m1v1i + m2v2i = m1v1f + m2v2f.
Only for elastic collisions do we also have (1/2)m1v1i2 + (1/2)m2v2i2 = (1/2)m1v1f2 + (1/2)m2v2f2.
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