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# Initial velocities of two particles

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Two particles, of mass 1 kg and 3 kg, are traveling towards each other with velocities of 100 m/s and -40 m/s respectively. Using the laws of physics (e.g. conservation of energy & momentum) calculate the following:
a) What are the initial energies of the particles?
b) What are the final velocities of the particles?
c) Which particle gained energy, and which lost energy?

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The initial velocities of two particles are given. The particles of gained energy are determined.

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Two particles, of mass 1 kg and 3 kg, are traveling towards each other with velocities of 100 m/s and -40 m/s respectively. Using the laws of physics (e.g. conservation of energy & momentum) calculate the following:
a) What are the initial energies of the particles?
b) What are the final velocities of the particles?
c) Which particle gained energy, and which lost energy?

a) The initial energies are given by the equation:
Ei = 0.5*m*v2

For particle 1:
Ei = 0.5*m¬1*v12
= 0.5*(1 kg)*(100 m/s)2
= (0.5 kg)*(10,000 m2/s2)
= 5000 kg*m2/s2

The unit [kg*m2/s2] is not a familiar unit of energy, so we should check to see if it is correct:
kg*m2/s2 = m*(kg*m/s2) = m*N = J

So we see that [kg*m2/s2] = [J], (joule) which is the SI unit of energy.

For particle 2:
Ei = 0.5*m2*v22
= 0.5*(3 kg)*(-40 m/s)2
= (1.5 kg)*(1600 m2/s2)
= 2400 J

b) The conservation of momentum & energy say that
Pi = Pf
(the initial momentum equals the final momentum)

Ei = Ef
(the initial energy equals the final ...

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