Density & Pressure Notes
Density
Definition: Density is defined as the mass per unit volume of a material.
Formula: ( \rho = \frac{m}{V} )
Where:
( \rho ) = density (kg/m³)
( m ) = mass (kg)
( V ) = volume (m³)
Formula Triangle:
Use the formula triangle to rearrange for unknown values by covering up the desired quantity.
Low vs. High Density Materials
Objects made from low-density materials have a low mass.
Similarly sized objects made from high-density materials have a high mass.
Examples:
A bag of feathers is lighter than a bag of metal.
A balloon has a lower density than a small bar of lead.
Density Comparisons:
Gases are less dense than solids because gas particles are more spread out (same mass over a larger volume).
Measurement of Density
Units Depend on Mass and Volume:
If mass is in grams (g) and volume in cm³, density is in g/cm³.
If mass is in kg and volume in m³, density is in kg/m³.
Volume Calculation for Density
o Common 3D Shapes: Use geometrical formulas to calculate the volume of regular shapes to find density.
Worked Example:
A paving slab with a mass of 73 kg and dimensions 0.04 m x 0.5 m x 0.85 m:
Mass: ( m = 73 \text{ kg} )
Volume: ( V = 0.04 \times 0.5 \times 0.85 = 0.017 \text{ m}^3 )
Calculate density: ( \rho = \frac{m}{V} = \frac{73}{0.017} = 4294 \text{ kg/m}^3 )
Rounded to two significant figures: 4300 kg/m³.
Core Practical: Determining Density
Apparatus:
Regular/irregular objects, liquid (e.g., sugar or salt solution), 30 cm ruler, Vernier calipers, micrometer, digital balance, displacement can, and measuring cylinders.
Resolution of Equipment:
Ruler: 1 mm
Vernier calipers: 0.01 mm
Micrometer: 0.001 mm
Digital balance: 0.01 g
Experiment 1: Regularly Shaped Objects
Method:
Measure mass using a digital balance.
Measure dimensions with a ruler, calipers, or micrometer.
Calculate volume using appropriate formulae based on shape.
Record results in a table for multiple trials to reduce random error.
Experiment 2: Irregularly Shaped Objects
Method:
Measure mass of object using a digital balance.
Use a Eureka can to measure water displacement; volume of displaced water = volume of the object.
Record mass and volume in a results table.
Experiment 3: Measuring Density of Liquids
Method:
Measure the empty mass of a measuring cylinder.
Fill cylinder with liquid and record new mass.
Calculate mass of liquid and then density using density formula.
Evaluating Experiments
Systematic Errors:
Ensure the digital balance is zeroed before measurements.
Random Errors:
Take multiple readings for dimensions to minimize error due to measurements.
Handle objects carefully to prevent displacement errors in water.
Pressure
Definition: Pressure is the force per unit area.
Formula: ( P = \frac{F}{A} )
Where
( P ) = pressure (Pa)
( F ) = force (N)
( A ) = area (m²)
Applications of Pressure
Drawing Pins: Push down on a small area, concentrating force and creating pressure that allows it to penetrate surfaces.
Tractors: Large tires spread weight over a larger area, reducing pressure and preventing sinking.
Nails: Sharp points concentrate force and allow nails to penetrate surfaces easily.
Pressure in Liquids
When an object is immersed in a liquid, pressure is exerted evenly across its surface and in all directions.
Pressure Differences: The deeper the object, the higher the pressure.
Pressure Equation: ( P = h \times \rho \times g )
Where:
( P ) = pressure (Pa)
( h ) = depth (m)
( \rho ) = density of the fluid (kg/m³)
( g ) = gravitational field strength (N/kg)
Worked Example for Pressure in Liquids
Problem: Calculate the depth of water if pressure is 20 kPa, water density is 1000 kg/m³, and gravitational field strength is 9.8 N/kg.
Convert pressure: 20 kPa = 20,000 Pa.
Use formula: ( h = \frac{P}{\rho \times g} = \frac{20000}{1000 \times 9.8} = 2.0408 m ).
Rounded value: 2.0 m.
Final Tips
Always take care of units during calculations, especially with large pressures and convert where necessary.
Revisit the pressure equation and practice rearranging for different variables.