Bang bang, I hit the ground...

During a busy day at the restaurant, a chef accidentally knocks two eggs off his table. The first one of lands on the hard floor and breaks into lots of tiny pieces, while the second lands on the soft carpet nearby, and comes to a full stop without breaking nor bouncing.

What can we say about the impulses endured by the two eggs, I 1 \vec{I}_{1} and I 2 \vec{I}_{2} ?


Taken from the 2014 Italian Physics Olympiad - Level 1

There is not enough information I 1 > I 2 \vec{I}_{1} > \vec{I}_{2} I 1 < I 2 \vec{I}_{1} < \vec{I}_{2} I 1 = I 2 \vec{I}_{1} = \vec{I}_{2}

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2 solutions

Petru Lupsac
Dec 22, 2014

Impulse can be written as I = F Δ t = m Δ v \vec{I} = \vec{F} \cdot \Delta t = m \cdot \vec{\Delta v}

Since both eggs are identical, and they fall from the same height, their speed right before the impact will be the same, and after the impact they both come to a full stop. Therefore, Δ v 1 = Δ v 2 I 1 = I 2 \Delta \vec{v_{1}} = \Delta \vec{v_{2}} \implies \vec{I_{1}} = \vec{I_{2}}

Iqbal Sambora
Dec 18, 2014

Impulse (I) = F . (t2-t1) F1=F2 So I1=I2

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