define elastic collision.discuss it for two bodies in one dimension .calculate velocities of the bodies after collision .discuss special cases also
Answers
Answer:
An elastic collision is an encounter between two bodies in which the total kinetic energy of the two bodies remains the same.
the elastic collision of two objects moving along the same line—a one-dimensional problem. An elastic collision is one that also conserves total kinetic energy, in addition to the total momentum. Figure illustrates an elastic collision in which kinetic energy and momentum are conserved.
ELASTIC COLLISION
An elastic collision is one that conserves total kinetic energy.
The system of interest contains a smaller mass m sub1 and a larger mass m sub2 moving on a frictionless surface. M sub 2 moves with velocity V sub 2 and momentum p sub 2 and m sub 1 moves behind m sub 2, with velocity V sub 1 and momentum p sub 1 toward the right direction. P 1 plus P 2 equals p total. The net force is zero. After collision m sub 1 moves toward the left with velocity V sub 1 while m sub 2 moves toward the right with velocity V sub 2 on the same frictionless surface. The momentum of m sub 1 becomes p 1 prime and m 2 becomes p 2 prime now. P 1 prime plus p 2 prime equals p total.
An elastic one-dimensional two-object collision. Momentum and internal kinetic energy are conserved.
Now, to solve problems involving one-dimensional elastic collisions between two objects we can use the equations for conservation of momentum and conservation of internal kinetic energy. First, the equation for conservation of momentum for two objects in a one-dimensional collision is
p1+p2=p'1+p'2(Fnet=0)
or
m1v1+m2v2=m1v'1+m2v'2(Fnet=0),
where the primes (') indicate values after the collision. By definition, an elastic collision conserves total kinetic energy, and so the sum of kinetic energies before the collision equals the sum after the collision. Thus,
12m1v12+12m2v22=12m1v'12+12m2v'22(two-object elastic collision)
expresses the equation for conservation of total kinetic energy in a one-dimensional collision.
Calculating Velocities Following an Elastic Collision
Calculate the velocities of two objects following an elastic collision, given that
m1=0.500 kg,m2=3.50 kg,v1=4.00 m/s, andv2=0.
Explanation:
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