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Egg on a Sheet
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===Full Explanation=== Force, Momentum and Impulse are all related to each other by the following equations: {| class="wikitable" style="color:black; background-color:#ddd; text-align: center; margin-right: auto" | Momentum | '''p''' = '''m''' * '''v''' | d/dt '''p''' = '''m''' * '''v/t''' = '''m''' * '''a''' = '''F''' |- | Force | '''F''' = '''m''' * '''a''' | '''β« F''' dt = '''F''' * '''t<sub>f</sub>''' - '''F''' * '''t<sub>i</sub>''' = '''F''' * β'''t''' = '''I''' |- | Impulse | '''I''' = '''F''' * β'''t''' | '''I''' = '''m''' * '''a''' * β'''t''' = ('''m''' * '''v<sub>f</sub>''') - ('''m''' * '''v<sub>i</sub>''') = β'''p''' |} Momentum is when a mass has a velocity to it. Force is when a mass has an acceleration to it. The derivative of momentum is force, since the derivative of a velocity is equal to acceleration. The integral of force is called impulse. ''Impulse'' is a change in momentum over time, and can be either positive (indicating an increase in momentum) or negative (indicating a decrease in momentum). If there is no change in momentum over time, then the impulse is equal to zero, and you would use the basic momentum equation. By connecting these three equations, we can accurately map out the situation that happens with the egg. {| class="wikitable" style="color:black; background-color:#ddd; text-align: center; margin-right: auto" |+ Tracing the Egg Throw | '''Part of Movement''' | Egg Wind up | Egg Release | Egg Traveling Through Air | Egg Hits the Sheet | Egg Stopped by Sheet |- | '''Movement Type''' | Force (Positive) | Impulse (Positive) | Momentum | Force (Negative) | Impulse (Negative) |- | '''Equation''' | '''F''' = '''m''' *'''a'''(+) | '''I''' = ('''m''' * '''v<sub>f</sub>'''(+)) - ('''m''' * '''v<sub>i</sub>'''(0)) = ('''m''' * '''v<sub>f</sub>''') - 0 | '''I''' = 0 since '''v<sub>f</sub>''' = '''v<sub>i</sub>''', so p = '''m''' * '''v''' | -'''F''' = '''m''' *'''a'''(-) | -'''I''' = (-'''F''' * '''t<sub>f</sub>'''(+)) - (-'''F''' * '''t<sub>i</sub>'''(0)) = (-'''F''' * '''t<sub>f</sub>''') - 0 |} When the egg strikes the sheet at the end, it does not break because of the time it takes for the egg to fully stop. We normally are used to seeing impulses acting on things instantly, like if the egg were to be dropped on the floor. This is because of the hard surface not allowing any recoil to happen, and therefore the eggshell having to try and absorb all of the damage from the strike. With a hard surface, the deceleration is too fast for the egg to handle. The sheet allows give, and with that the egg can take a slightly longer time to stop. This time difference, even though it seems to be only a little bit longer, makes a big difference in how well the egg can handle the force of impact. With a longer stop time, the egg experiences less force per time interval, which allows the egg to avoid breaking!
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