Solved Examples: Calculating Pressure in Fluids and Solids

📚 Quick Study Guide

• 🌊 Pressure in Fluids: Pressure at a depth $h$ in a fluid is given by $P = P_0 + \rho gh$, where $P_0$ is the atmospheric pressure, $\rho$ is the fluid density, and $g$ is the acceleration due to gravity.
• 🧱 Pressure in Solids: Pressure is defined as force per unit area: $P = \frac{F}{A}$.
• 📏 Units of Pressure: Pascal (Pa) is the SI unit of pressure, where 1 Pa = 1 N/m². Other units include atm, bar, and psi.
• ⚖️ Pascal's Law: Pressure applied to an enclosed fluid is transmitted undiminished to every portion of the fluid and the walls of the containing vessel.
• 💡 Archimedes' Principle: The buoyant force on an object submerged in a fluid is equal to the weight of the fluid displaced by the object.

🧪 Practice Quiz

1. Question 1: A rectangular block of wood has dimensions 2m x 1m x 0.5m and a weight of 6000 N. What is the pressure exerted by the block on the ground if it rests on its largest face?
   1. 1000 Pa
   2. 2000 Pa
   3. 3000 Pa
   4. 6000 Pa
2. Question 2: A submarine is submerged at a depth of 200m in seawater (density = 1025 kg/m³). What is the absolute pressure experienced by the submarine? (Assume atmospheric pressure is 101325 Pa and g = 9.8 m/s²)
   1. 1.10 x 10^6 Pa
   2. 2.11 x 10^6 Pa
   3. 3.00 x 10^6 Pa
   4. 4.50 x 10^6 Pa
3. Question 3: A hydraulic lift has two pistons with areas of 0.01 m² and 0.5 m². If a force of 100 N is applied to the smaller piston, what force will be exerted by the larger piston?
   1. 2000 N
   2. 5000 N
   3. 100 N
   4. 50 N
4. Question 4: A cube of aluminum with side length 0.1 m is submerged in water. The density of aluminum is 2700 kg/m³, and the density of water is 1000 kg/m³. What is the buoyant force acting on the cube?
   1. 9.8 N
   2. 19.6 N
   3. 26.46 N
   4. 2.7 N
5. Question 5: A cylindrical tank has a radius of 2 meters and is filled with water to a height of 5 meters. What is the gauge pressure at the bottom of the tank? (Density of water = 1000 kg/m³, g = 9.8 m/s²)
   1. 49,000 Pa
   2. 98,000 Pa
   3. 147,000 Pa
   4. 196,000 Pa
6. Question 6: A 50 N force is applied to an area of 5 $m^2$. What is the pressure?
   1. 5 Pa
   2. 10 Pa
   3. 250 Pa
   4. 0.1 Pa
7. Question 7: A block with a weight of 100 N is placed on a table. The block measures 0.5m x 0.25m. What is the pressure exerted on the table?
   1. 200 Pa
   2. 400 Pa
   3. 600 Pa
   4. 800 Pa