If an egg is dropped with a cushion, I know that the cushion will reduce its impulse.
Since impulse = change in momentum ($J = \Delta p$), would the change in momentum also be affected by the cushion?
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1 Answer
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The impulse applied to the egg does not change because the egg has the same starting and ending values for its momentum (e.g. if it starts with $p= 1 \frac{kg\,m}{s}$ and ends with $p= 0 \frac{kg\,m}{s}$ then the impulse would have to have a magnitude of $1N\cdot s$ regardless of how much time is between the "start" and "end").
Rather, the maximum force applied to the egg would be reduced, because impulse is equal to the integral of force with respect to time and the pillow applies a weaker force across a longer period of time (e.g. $0.5N$ applied for $2s$ gives $1N\cdot s$ of impulse and $1N$ applied for $1s$ also gives $1N\cdot s$)
Because the impulse does not change, the change in momentum also does not change.
