Newton's Laws: Sharp vs. Dull Knives

[tornzaer]

Homework Statement

Why does a sharp knife cut better than a dull knife? Explain using Newton's Laws.

The Attempt at a Solution

1st Law: Since the sharper knife has less surface area, it keeps more better than the dull knife. The friction is less.

2nd Law: Less surface area on knife means more acceleration means more force.

3rd Law: Less opposing force because of less surface area?

Please correct me if I'm missing something. Thanks.

 

[physics girl phd]

First: List Newton's laws and include them in yuor answer (chances are if this is graded, the grader wants to see these laws explicitly stated). What does the first law say? How does this relate to EACH knife, or what, if anything, does it have to say about the properties of the forces exerted by or on each knife? then move on to the second...

In each part: always specify WHICH knife you are talking about, and specifically compare it to the other knife... right now your answer is (especially in parts 2 and 3), to tell the truth, pretty unclear about which knife you are discussing, and then in part 1, you seem to be missing a word or two (it keeps more _____ better?).

Also: I end to personally say the problem has less to do with friction (which is best to think of in terms on sliding ON a surface or resisting sliding, in the case of kinetic friction) and more to do with what might be better called "resistance" (like air resistance, except in this case, it a mass other than an air mass). Air resistance does tend to relate to area. Friction perhaps to your surprise does not relate to area.

 

[baba89]

Your understanding of Newton's Laws is correct, but there are a few more factors to consider when explaining why a sharp knife cuts better than a dull knife.

Firstly, the 1st Law, also known as the Law of Inertia, states that an object at rest will remain at rest unless acted upon by an external force. In this case, the external force is the force applied to the knife to cut through an object. A sharp knife has a smaller surface area, which means that less force is needed to overcome its inertia and start cutting. This is because the sharp edge of the knife has a smaller contact area with the object, reducing the amount of force needed to cut through it.

Secondly, the 2nd Law, also known as the Law of Acceleration, states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. In other words, the sharper knife, with less surface area, has less mass and therefore requires less force to accelerate and cut through an object.

Lastly, the 3rd Law, also known as the Law of Action and Reaction, states that for every action, there is an equal and opposite reaction. In the case of cutting with a knife, the action is the force applied by the knife to the object, and the reaction is the force exerted by the object back onto the knife. A sharper knife, with less surface area, will have less resistance from the object, resulting in a smaller opposing force. This allows the knife to cut through the object more easily and with less effort.

In summary, Newton's Laws explain why a sharp knife cuts better than a dull knife by considering factors such as inertia, mass, and resistance. The smaller surface area of a sharp knife reduces the amount of force needed to overcome its inertia and cut through an object, making it more efficient and effective in cutting.