How does Newton's Third Law of Motion apply to stepping on a cockroach?

[z.js]

Alright, so it goes like this: you see A Cockroach strolling in the Kitchen. So you go up right in front of the Oven where The Cockroach is and prepare to step on it.() But wait()! Newton's Third Law of Motion won't have it! The Cockroach would exert an equal and opposite Force on your Foot, thus being invincible.().
My physics book said something about this: the equal opposing forces act on different objects. But how does it apply to this situation? Does the floor also exert a force?

 

[A.T.]

The Cockroach would exert an equal and opposite Force on your Foot,

Yes

thus being invincible

No. Equal force doesn't mean equal acceleration (when different masses are involved), or equal damage (when different materials are involved). The force needed to squash a cockroach is tiny, so the equal-opposite force merely causes a negligible deceleration of your leg, but is not sufficient to stop it.

But try to squash a lego brick with you bare foot.

 

[tycoon515]

Your foot and the floor are (approximately) rigid bodies in that they do not deform. The cockroach on the other hand is not a rigid body; it deforms relatively easily. As your foot lands on the cockroach, it applies a downward force that propagates through the cells that make up the cockroach though not all of this force is sent directly down through it. The staggered arrangement of the cells of the cockroach means that some of this force is redirected sideways, acting to push its cells outward, causing the cockroach to flatten. Your foot applies a negative, or downward, force on the cockroach, and the ground applies a positive, or upward, force slightly less in magnitude on the cockroach. The net force on the cockroach is negative, so its center of mass accelerates downward, which makes sense since it flattens as its cells spread out. Another way to look at it is that the ground need not supply as great a force because some of the force your foot applies is used to spread out the cockroach's cells, and the cells of the cockroach touching the floor are left with slightly less vertical force than those in contact with your foot. The cockroach applies the same amount of force to the floor as the floor applies to the cockroach, except downward. Likewise, the cockroach applies the same amount of force to your foot as your foot applies to the cockroach, except upward. Your foot does positive work on the cockroach by displacing its center of mass negatively, the same direction of the force your foot applies. However, the floor does negative work on the cockroach since the cockroach's center of mass displaces negatively while the floor exerts a positive force on the cockroach. The cockroach itself does negative work on your foot since your foot continues to displace negatively, opposite in direction of the force the cockroach applies to it, accelerating it positively (i.e. slowing its descent). The cockroach does zero work on the floor since it does not displace the floor at all.