Scelta multipla
Under which condition is the total momentum of a system conserved during a collision?
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11. Momentum & Impulse
Intro to Conservation of Momentum
Scelta multipla
According to the law of conservation of momentum, what must the total (momentum) of the system be after two train cars collide in the absence of external forces?
A
The total after the collision must be .
B
The total after the collision must be equal to the total before the collision.
C
The total after the collision must be greater than before the collision.
D
The total after the collision must be less than before the collision.
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Recall the law of conservation of momentum, which states that in the absence of external forces, the total momentum of a system remains constant.
Define the total momentum before the collision as the sum of the momenta of the two train cars: \(\mathbf{p}_{\text{total, before}} = \mathbf{p}_1 + \mathbf{p}_2\).
Similarly, define the total momentum after the collision as \(\mathbf{p}_{\text{total, after}} = \mathbf{p}_1' + \mathbf{p}_2'\), where the primes denote momenta after the collision.
According to the conservation law, set the total momentum before the collision equal to the total momentum after the collision: \(\mathbf{p}_{\text{total, before}} = \mathbf{p}_{\text{total, after}}\).
Conclude that the total momentum after the collision must be equal to the total momentum before the collision, regardless of the details of the collision, as long as no external forces act on the system.
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