(a) Explain the difference between elastic and inelastic collisions, stating wha
ID: 2222179 • Letter: #
Question
(a) Explain the difference between elastic and inelastic collisions, stating what is conserved ineither case.
(b) A particle of mass mo, travelling at speed vo, strikes a stationary particle of mass 2mo. As a
result, the particle of mass mo is de?ected through 45 degres and has a ?nal speed of vo=2. Find
the speed (expressed as a fraction of vo) and direction of the particle of mass 2mo after this
collision.
(c) Determine whether kinetic energy was conserved in the above collision.
(d) In an accident at a road intersection, a car (of mass 2 tonnes) travelling south across the
intersection crashes into a lorry (mass 6 tonnes) travelling west. They tangle and skid off the
road together, heading exactly south-west.
(i) Draw and label a sketch of this accident, showing the motions of car, lorry and the centre
of mass, before and after the crash. What can you say
Explanation / Answer
A) A perfectly elastic collision is defined as one in which there is no loss of kinetic energy in the collision. An inelastic collision is one in which part of the kinetic energy is changed to some other form of energy in the collision. Any macroscopic collision between objects will convert some of the kinetic energy into internal energy and other forms of energy, so no large scale impacts are perfectly elastic. Momentum is conserved in inelastic collisions, but one cannot track the kinetic energy through the collision since some of it is converted to other forms of energy. Collisions in ideal gases approach perfectly elastic collisions, as do scattering interactions of sub-atomic particles which are deflected by the electromagnetic force. Some large-scale interactions like the slingshot type gravitational interactions between satellites and planets are perfectly elastic. Collisions between hard spheres may be nearly elastic, so it is useful to calculate the limiting case of an elastic collision. The assumption of conservation of momentum as well as the conservation of kinetic energy makes possible the calculation of the final velocities in two-body collisions. An elastic collision is defined as one in which both conservation of momentum and conservation of kinetic energy are observed. This implies that there is no dissipative force acting during the collision and that all of the kinetic energy of the objects before the collision is still in the form of kinetic energy afterward. For macroscopic objects which come into contact in a collision, there is always some dissipation and they are never perfectly elastic. Collisions between hard steel balls as in the swinging balls apparatus are nearly elastic. "Collisions" in which the objects do not touch each other, such as Rutherford scattering or the slingshot orbit of a satellite off a planet, are elastic collisions. In atomic or nuclear scattering, the collisions are typically elastic because the repulsive Coulomb force keeps the particles o c) yes d)
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