Pressure in Solids Flashcards

Introduction to Pressure in Science

• In everyday speech, the term "pressure" is frequently used interchangeably with words like "weight" or "force."

• In scientific terms, pressure is a distinct concept from weight.

• Pressure is defined as how much force is applied to a certain area.

The Pressure Formula and Units

• Pressure is calculated using the following relationship:     $\text{Pressure} = \frac{\text{Force}}{\text{Area}}$

• While initial discussions might use the term "Weight" as the numerator (Weight / Area), the formal scientific formula identifies the numerator as Force (measured in Newtons).

• The units for pressure are derived from the formula:

  • \text{Newtons per square centimeter (N/cm^2)}

  • \text{Newtons per square meter (N/m^2)}

  • $\text{Pascal (Pa)}$ is also an accepted and common unit for measuring pressure.

Practical Examples and Scientific Explanations

• Sharp vs. Blunt Objects:

  • A sharp knife cuts more effectively than a blunt one because the cutting edge has a much smaller surface area. This results in a much higher pressure being exerted on the object being cut for the same amount of force.

  • Other tools that require sharpness to function effectively include pencils, scissors, and needles.

• The Drawing Pin Example:

  • It is painful to press the "pointy" end of a drawing pin into your finger but not the flat end. This is because the surface area of the point is extremely small, creating high pressure against the skin even with a small force.

  • Calculation Example: If a drawing pin is pushed with a force of $50\,N$ into an area of $0.5\,cm^2$, the pressure is calculated as:         $\text{Pressure} = \frac{50\,N}{0.5\,cm^2} = 100\,N/cm^2$

• Skis on Snow:

  • Skis are used on snow to increase the surface area over which a person's weight (force) is distributed. By increasing the area, the pressure on the snow is reduced, preventing the skier from sinking.

  • Calculation Example: A skier exerting a force of $75\,N$ with skis covering an area of $30\,cm^2$ has a pressure of:         $\text{Pressure} = \frac{75\,N}{30\,cm^2} = 2.5\,N/cm^2$

• Camel Adaptations:

  • Camels have evolved with large, wide feet. This is an adaptation to their environment that allows them to walk on soft sand without sinking, as their weight is spread over a larger surface area, thereby reducing the pressure exerted on the ground.

• Stool Feet Scenario:

  • If a person is sitting on a stool and moves it so a stool foot lands on someone's toe, it causes significantly more pain than if that person simply stepped on the toe barefoot. This is because the stool foot has a very small surface area compared to a human foot, concentrating the combined force of the person and the stool into a high-pressure point.

Relationship Between Variables

• Force and Pressure: These variables have a direct relationship.

  • As Force increases ($\uparrow$), Pressure increases ($\uparrow$).

  • As Force decreases ($\downarrow$), Pressure decreases ($\downarrow$).

• Surface Area and Pressure: These variables have an inverse relationship.

  • As Surface Area increases ($\uparrow$), Pressure decreases ($\downarrow$).

  • As Surface Area decreases ($\downarrow$), Pressure increases ($\uparrow$).

Case Study: Comparative Pressure (Elephant vs. Human in Heels)

• Visual Context: A cartoon depicts a man shouting "GET THAT WOMAN OFF MY FLOOR!" to demonstrate the extreme pressure caused by specific footwear.

• Unit Conversion Note: There are $10,000\,cm^2$ in $1\,m^2$.

• Elephant Statistics:

  • Mass of an African elephant: $5,000\,kg$.

  • Weight (Force) of the elephant: $50,000\,N$.

  • Area of one foot: $0.1\,m^2$.

  • Total area of four feet: $4 \times 0.1\,m^2 = 0.4\,m^2$.

  • Pressure in $N/m^2$: $\frac{50,000\,N}{0.4\,m^2} = 125,000\,N/m^2$.

  • Pressure in $N/cm^2$: $\frac{125,000\,N/m^2}{10,000} = 12.5\,N/cm^2$.

• Human Statistics (Standing Barefoot):

  • Average Force: approx. $500\,N$.

  • Area of two feet: approx. $280\,cm^2$.

  • Pressure on 2 feet: $\frac{500\,N}{280\,cm^2} \approx 1.78\,N/cm^2$ ($17,800\,N/m^2$).

  • Notice: When standing on one foot instead of two, the area is halved, which causes the pressure to double.

• Human Statistics (In Stiletto Heels):

  • Force: approx. $500\,N$.

  • Area of two heels: approx. $2\,cm^2$ (assuming approximately $1\,cm^2$ per heel).

  • Pressure in heels ($N/cm^2$): $\frac{500\,N}{2\,cm^2} = 250\,N/cm^2$.

  • Pressure in heels ($N/m^2$): $2,500,000\,N/m^2$.

• Grand Comparison:

  • An elephant barefoot ($12.5\,N/cm^2$) exerts more pressure than a human barefoot ($1.78\,N/cm^2$).

  • However, a human in stiletto heels ($250\,N/cm^2$) exerts 20 times more pressure on the floor than an elephant.

Problem Solving Challenge: The Box and the Table

• Scenario: A box weighing $150\,N$ has dimensions $1.5\,m \times 0.4\,m \times 30\,cm$ ($0.3\,m$). Which side(s) can be placed on a table to ensure the table does not break?

• Logic: The side with the largest surface area will exert the lowest pressure.

• Calculation - Biggest Side:

  • Area: $1.5\,m \times 0.4\,m = 0.6\,m^2$.

  • Pressure: $\frac{150\,N}{0.6\,m^2} = 250\,N/m^2$.

  • Result: This side ensures the table does not break.

• Calculation - Second Biggest Side:

  • Area: $1.5\,m \times 0.3\,m = 0.45\,m^2$.

  • Pressure: $\frac{150\,N}{0.45\,m^2} = 333.3\,N/m^2$.

  • Result: The table will break under this pressure.