Solved Examples of Pressure Calculations in Physics

📚 Quick Study Guide

• 📏 Definition of Pressure: Pressure is defined as the force acting perpendicularly on a unit area. It's a scalar quantity.
• 🔢 Formula for Pressure: The formula for pressure ($P$) is given by: $P = \frac{F}{A}$, where $F$ is the force and $A$ is the area.
• ⚖️ Units of Pressure: The SI unit of pressure is Pascal (Pa), which is equivalent to Newtons per square meter (N/m²). Other common units include atmospheres (atm) and pounds per square inch (psi).
• 💧 Fluid Pressure: For fluids at a certain depth ($h$), the pressure is given by: $P = \rho gh$, where $\rho$ is the density of the fluid, and $g$ is the acceleration due to gravity.
• 🌡️ Atmospheric Pressure: The pressure exerted by the weight of the atmosphere above a given point. At sea level, it's approximately 101325 Pa.
• 💡 Pascal's Law: Pressure applied to a confined fluid is transmitted equally throughout the fluid. This principle is used in hydraulic systems.

🧪 Practice Quiz

1. What is the pressure exerted by a force of 100 N acting on an area of 2 $m^2$?
   1. 50 Pa
   2. 100 Pa
   3. 200 Pa
   4. 400 Pa
2. A fluid has a density of 1000 kg/m³ and a depth of 5 m. What is the pressure at that depth (assume g = 9.8 m/s²)?
   1. 49000 Pa
   2. 9800 Pa
   3. 5000 Pa
   4. 19600 Pa
3. If the pressure on a surface is 200 Pa and the area is 4 $m^2$, what is the force acting on the surface?
   1. 50 N
   2. 200 N
   3. 400 N
   4. 800 N
4. Which of the following is the correct unit for pressure?
   1. Newton (N)
   2. Kilogram (kg)
   3. Pascal (Pa)
   4. Meter (m)
5. According to Pascal's Law, what happens to the pressure applied to a confined fluid?
   1. It decreases.
   2. It increases.
   3. It remains constant.
   4. It is transmitted equally throughout the fluid.
6. What is the approximate value of atmospheric pressure at sea level in Pascals?
   1. 101325 Pa
   2. 50000 Pa
   3. 200000 Pa
   4. 10000 Pa
7. A hydraulic lift has an input piston with an area of 0.1 $m^2$ and an output piston with an area of 1 $m^2$. If a force of 100 N is applied to the input piston, what is the force exerted by the output piston?
   1. 10 N
   2. 100 N
   3. 1000 N
   4. 10000 N