Which explicit definition matches this sequence? an={10,if n=1an−1−4,if n>1 A. an = 10 + 4(n – 1) B. an = 10 – 4(n – 1) C. an
1 answer:
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a. The magnitude of the change of the momentum of the 5-kg ball is equal to the magnitude of the change of momentum of the 10-kg ball.
c. The magnitude of the change of velocity the 5-kg ball experiences is greater than that of the 10-kg ball.
Explanation:
For an inelastic collision:
- The total momentum of the system is conserved
- The total kinetic energy of the system is not conserved
Using these facts, let's now analyze each statement given.
a. The magnitude of the change of the momentum of the 5-kg ball is equal to the magnitude of the change of momentum of the 10-kg ball. --> TRUE. Since the total momentum is conserved, we can write:
where
is the initial momentum of the 5-kg ball
is the final momentum of the 5-kg ball
is the final momentum of the 10-kg ball
The equation can be rewritten as
which is equivalent to
which means that the magnitude of the change of momentum of the two balls is the same.
b. Both balls lose all their momentum since the collision is inelastic. --> FALSE, the 10-kg ball gains momentum, so it does not lose it.
c. The magnitude of the change of velocity the 5-kg ball experiences is greater than that of the 10-kg ball. --> TRUE. We already said that the magnitude of the change in momentum of the two balls is the same. However, it can be written as
where m is the mass of the ball and its change in velocity. Therefore, the 5-kg ball (which has smaller mass) will have a larger
, so a larger change in velocity.
d. The magnitude of the change of velocity the 5-kg ball experiences is equal to that of the 10-kg ball. --> FALSE, as we discussed in c).
e. The magnitude of the change of velocity the 5-kg ball experiences is less than that of the 10-kg ball. --> FALSE, as we discussed in c).
Learn more about change in momentum:
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