please explain
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Hi! Sorry for my bad English, I'm Italian ...
Calling m1 mass of 4 kg and m2 mass of 16 kg, we can write:
The kinetics energy KE, are:
KE1 = 1/2 * m1 * v1² = 0.5 * 4 * v1²
KE2 = 1/2 * m2 * v2² = 0.5 * 16 * v2²
But KE1 = KE2 = KE, then:
KE = 1/2 * m1 * v1² = 0.5 * 4 * v1²
KE = 1/2 * m2 * v2² = 0.5 * 16 * v2²
v1 = √(2KE / 0.5 * 4) = √(KE / 4) = 1/2 * √(KE)
v2 = √(2KE / 0.5 * 16) = √(KE / 16) = 1/4 * √(KE)
momentum = m * v
momentum ratio (Mr) is:
Mr = m1 * v1 / (m2 * v2)
replacing values, we have:
Mr = 4 * 1/2 * √(KE) / [16 * 1/4 * √(KE)]
Mr = 2 * √(KE) / [4 * √(KE)]
Mr = 2/4 = 1/2
Obviously if we invert momentums, we have:
Mr = m2 * v2 / (m1 * v1)
Then:
Mr = 4 * √(KE) / [2 * √(KE)] = 2
bye
Quasar
Calling m1 mass of 4 kg and m2 mass of 16 kg, we can write:
The kinetics energy KE, are:
KE1 = 1/2 * m1 * v1² = 0.5 * 4 * v1²
KE2 = 1/2 * m2 * v2² = 0.5 * 16 * v2²
But KE1 = KE2 = KE, then:
KE = 1/2 * m1 * v1² = 0.5 * 4 * v1²
KE = 1/2 * m2 * v2² = 0.5 * 16 * v2²
v1 = √(2KE / 0.5 * 4) = √(KE / 4) = 1/2 * √(KE)
v2 = √(2KE / 0.5 * 16) = √(KE / 16) = 1/4 * √(KE)
momentum = m * v
momentum ratio (Mr) is:
Mr = m1 * v1 / (m2 * v2)
replacing values, we have:
Mr = 4 * 1/2 * √(KE) / [16 * 1/4 * √(KE)]
Mr = 2 * √(KE) / [4 * √(KE)]
Mr = 2/4 = 1/2
Obviously if we invert momentums, we have:
Mr = m2 * v2 / (m1 * v1)
Then:
Mr = 4 * √(KE) / [2 * √(KE)] = 2
bye
Quasar
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16kg of mass body will have the momentum twice the momentum of 4kg mass body. Because, 16kg of mass body can have just half the velocity of 4kg mass body's velocity to maintain the KE equal to the 4kg mass.
Or else, A body having squared the mass of other body just needs to have the velocity that is half the times of the other body, in order to keep the KE equal for both.
Or else, A body having squared the mass of other body just needs to have the velocity that is half the times of the other body, in order to keep the KE equal for both.