Chapter 9, Problem 1E

Why are sharp knives more effective than dull knives (Hint: think about the definition of pressure)?

Interpretation Introduction

Interpretation:The reason should be determined for more effectiveness of sharp knives incomparison to dull knives.

Concept introduction: Pressure is defined as force per unit area. It is mathematically represented as follows:

  $P=\frac{F}{A}$

Here, F is force and A is area.

Answer to Problem 1E

A sharp knife can exert a higher pressure in comparison to dull knife due to less surface area.

Explanation of Solution

Mathematically, pressure is defined as:

  $\text{P = }\frac{\text{F}}{\text{A}}$

A dull knife has a higher surface area than a sharp knife.

Since pressure is inversely proportional to surface area,a sharp knife cuts better due to the very small edge that has a small surface area. Thus, the pressure applied is larger.

Hence, sharp knives are more effective than dull knives.

Conclusion

Thus, a sharp knife with less surface area can exert a higher pressure for the same amount of force applied as compared to a dull knife.