Calculate the velocities of two bodies undergoing elastic collision in one dimension
Answers
ELASTIC COLLISION
An elastic collision is one that conserves internal kinetic energy.
INTERNAL KINETIC ENERGY
Internal kinetic energy is the sum of the kinetic energies of the objects in the system.
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.
Figure 1. 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 internal kinetic energy, and so the sum of kinetic energies before the collision equals the sum after the collision. Thus,
1
2
m
1
v
1
2
+
1
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m
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v
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2
=
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2
m
1
v
'
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+
1
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m
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v
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2
2
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two-object elastic collision
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expresses the equation for conservation of internal kinetic energy in a one-dimensional collision.
Answer:
Explanation:
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