Even with the same weight, pressing on a smaller area hurts or pierces──this is due to a difference in pressure. Let us consider the relationship between force and area.
Basic Knowledge
Pressure is the force acting per unit area and is expressed by the following formula:Pressure P [Pa] = Force F [N] ÷ Area S [m²]
In other words, P = F / S
The unit is the pascal (Pa), and 1 Pa = 1 N/m².
Example: When a person with a mass of 60kg stands flat on the floor (both feet), if the contact area with the ground is 0.04m² (the total for both feet),
F = 60 × 9.8 = 588 N
P = 588 ÷ 0.04 = 14700 Pa = 14.7 kPa.
If the same person stands on one high heel (contact area 0.0001m²), the pressure becomes approximately 5.88×10⁶Pa (approximately 400 times greater), which can damage the floor.
Pressure (force acting per unit area. P = F / S )
Pascal (Pa) (the unit of pressure. 1 Pa = 1 N/m² )
Hectopascal (hPa) (used in weather forecasts. 1 hPa = 100 Pa )
Atmospheric pressure (pressure caused by the weight of air. Approximately 1013 hPa = approximately 10万 Pa at sea level)
Barometer (a device that measures atmospheric pressure. Torricelli's experiment is famous)
Unit conversion (conversion from cm² to m² requires division by 10000)
Further Exploration (Background and Significance)
The concept of pressure is found everywhere around us.
・A kitchen knife has a thin blade → small contact area → large pressure with the same force → it cuts
・The tip of a thumbtack is pointed → for the same reason, it pierces a board
・Skis and caterpillar tracks increase the area → they do not sink into snow or soft ground
・A camel has wide soles → it does not sink in the desert
Atmospheric pressure is constantly approximately 1013 hPa(101300 Pa) around us. We are not crushed because the inside of our bodies also pushes outward with the same pressure. Changes in atmospheric pressure are related to weather and can be measured with a barometer. In Torricelli's experiment (1643), atmospheric pressure was measured from the fact that a column of mercury stopped at a height of approximately 76cm.
When calculating pressure, great care must be taken with units. Area must be expressed in m², not cm². Since 1m² = 10000cm², divide the value in cm² by 10000 to convert it to m².
- Pressure = force ÷ area
- Unit: Pa = N/m²
- 1 hPa = 100 Pa (used in weather forecasts)
- Atmospheric pressure ≒ 1013 hPa ≒ 10万 Pa
- Smaller area → greater pressure (knife・thumbtack)
- Larger area → lower pressure (skis・caterpillar tracks)
- 1m² = 10000cm² (take care with unit conversion)
Points to Note (Easily Confused)
① Force (N) and pressure (Pa) are different. Even with the same force, pressure changes with area. ② Unit conversions: 1m² = 10000cm², 1 hPa = 100 Pa. ③ Atmospheric pressure acts from all directions (from below, above, and the sides). ④ A 76cm column of mercury = 1 atmosphere is an important value in the history of science.
Practice
- Write the formula for finding pressure.
- Find the pressure when a force of 100N is applied to an area of 0.5m².
- What is the approximate atmospheric pressure in hPa?