If two bodies, one lighter than the other have the same Kinetic Energy. Which one will have greater Momentum?
回答 (2)
2018-03-17 6:53 pm
✔ 最佳答案
Suppose m₁ > m₂ …… [1]and (1/2)m₁v₁² = (1/2)m₂v₂² …… [2]
As both m₁ and m₂ are positive, from [1] :
√m₁ > √m₂ …… [3]
From [2] :
m₁v₁² = m₂v₂²
√(m₁v₁²) = √(m₂v₂²)
(√m₁)v₁ = (√m₂)v₂ …… {4}
[3] × [4] :
(√m₁)²v₁ > (√m₂)²v₂
Then, m₁v₁ > m₂v₂
The body with a greater mass would have greater momentum.
2018-03-17 6:33 pm
The one with the greater mass will have the greater momentum.
Ek = 1/2 m v^2
-> 2mEk = m^2 v^2
-> sqrt( 2 m Ek) = mv = momentum.
So for the same Ek the momentum rises according to the square root of the mass.
Ek = 1/2 m v^2
-> 2mEk = m^2 v^2
-> sqrt( 2 m Ek) = mv = momentum.
So for the same Ek the momentum rises according to the square root of the mass.
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