To analyze the situation, we need to consider the concept of impulse and how it relates to momentum and the time taken for an object to stop.
Impulse is defined as the change in momentum of an object, and it can be expressed as:
\[ \text{Impulse} = F \cdot \Delta t = \Delta p \]
where \(F\) is the average force applied, \(\Delta t\) is the time duration over which the force is applied, and \(\Delta p\) is the change in momentum.
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Egg A: When egg A lands on the tile floor, it comes to a quick stop. The change in momentum is equal to the momentum it had just before hitting the floor (downward) to zero (after hitting the floor). Since the floor is hard, the time (\(\Delta t_A\)) taken for the egg to stop is very short. Therefore, the impulse experienced by egg A is large, as it must compensate for the rapid change in momentum over a short time period.
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Egg B: Egg B lands on a foam pad, which compresses as the egg lands. The foam pad allows for a longer stopping time (\(\Delta t_B\)) because it absorbs the egg's energy and momentum more gradually compared to the tile floor. Even though the change in momentum for egg B is also equal to the momentum it carries just before landing (and goes to zero), the longer duration means that the average force exerted (and thus the impulse) is less intense over that time period compared to egg A.
In conclusion, while both eggs experience the same magnitude of change in momentum (since they drop from the same height and have the same mass) and thus the same impulse in terms of momentum change (both impulses are equal to the momentum just before impact), the magnitudes of the impulse experienced by egg A and egg B are different in terms of how quickly they happen. However, both impulses equal the same change in momentum, which means:
The magnitudes of the impulse on egg A and egg B are equal.
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