Chapter 10, Problem 4Q

To determine

The quantity that determines whether your skin is cut.

Explanation of Solution

Introduction:

The physical force that is exerted perpendicular to the surface of an object per unit are is defined as pressure. Mathematically given as:

  $P=\frac{F}{A}$

Here,

  $F$ is the force exerted on the object.

  $A$ is the surface area of the object.

Firstly, consider the sharp end of the pen, it has smaller surface area while the blunt end of the pen has a larger surface area compared to the sharp end. So, using the above expression for pressure, it depends on both force applied and the surface area. According to the given statement, force applied is same for both cases, so for larger area, pressure will be less but for smaller surface area the pressure will be greater.

Hence, pressure is the quantity that determines whether the skin is cut or not.

Conclusion:

Hence, the pressure is the required quantity which determines whether the skin is cut.