Question 12 (Mandatory) (5 points)
1 answer:
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Answer:
b) Betelgeuse would be times brighter than Sirius
c) Since Betelgeuse brightness from Earth compared to the Sun is the statement saying that it would be like a second Sun is incorrect
Explanation:
The start brightness is related to it luminosity thought the following equation:
(1)
where is the brightness,
is the star luminosity and
, the distance from the star to the point where the brightness is calculated (measured). Thus:
b) and
where
is the Sun luminosity (
) but we don't need to know this value for solving the problem.
is light years.
Finding the ratio between the two brightness we get:
c) we can do the same as in b) but we need to know the distance from the Sun to the Earth, which is . Then
Notice that since the star luminosities are given with respect to the Sun luminosity we don't need to use any value a simple states the Sun luminosity as the unit, i.e 1. From this result, it is clear that when Betelgeuse explodes it won't be like having a second Sun, it brightness will be 5 orders of magnitude smaller that our Sun brightness.
a) 779 kg m/s
The momentum of an object is given by:
p = mv
where
m is the mass of the object
v is its velocity
For the fullback before the collision,
m = 95 kg
v = 8.2 m/s
Therefore, his momentum was:
b) -779 kg m/s
After the collision, both the fullback and the tackle come to a stop: this means that their momentum after the collision is zero,
p' = 0
The initial momentum of the fullback was
p = 779 kg m/s
Therefore, his change in momentum is
where the negative sign indicates that the direction is opposite to the initial direction of motion.
c) -779 kg m/s
Here we can apply the law of conservation of momentum. In fact, the total momentum before and after the collision must be conserved. So we can write:
where
is the initial momentum of the fullback
is the initial momentum of the tackle
p' is the final combined momentum after the collision
We already know that
Therefore, we can find the tackle's original momentum:
where the negative sign indicates that the direction is opposite to the initial direction of motion of the fullback.
e) -6.1 m/s
To find the velocity of the tackle, we can use again the equation of the momentum:
p = mv
where here we have
is the original momentum of the tackle
m = 128 kg is his mass
Solving the equation for v, we find the tackle's original velocity:
So, he was moving at 6.1 m/s in the direction opposite to the fullback.