Core practicals: mechanics, materials and thermal

Core Practicals: Mechanics, Materials and Thermal

Welcome to your revision guide for the core practicals covering mechanics, materials, and thermal physics. In the Pearson Edexcel GCSE (9-1) Physics course, there is no separate coursework exam—instead, at least \(15\%\) of the marks across your written papers will test your understanding of experimental work (AO1, AO2, and AO3). Mastering these practicals means you can confidently pick up marks on experimental design, data analysis, graph skills, and evaluation!

Note: Other practical investigations are explored in the chapter Core practicals: waves, light and electricity.

1. Core Practical 2.19: Force, Mass and Acceleration

Aim of the Experiment

To investigate the relationship between resultant force, mass, and acceleration using trolleys, verifying Newton's Second Law: \(F = m \times a\).

Key Apparatus

• Ramp / runway and trolley
• Two light gates connected to a data logger (or one light gate with a double interrupt card)
• Pulley, string, and slotted masses on a hanger
• Balance (to measure mass)
• Ruler (to measure the card length and distances)

Method: Investigating Acceleration vs Force (Mass Kept Constant)

1. Measure the total mass of the trolley, string, and all hanging masses combined using a balance.
2. Prop up one end of the ramp slightly until the trolley just rolls at a constant speed when pushed gently. This counteracts friction.
3. Attach an interrupt card of known length to the trolley and position two light gates along the track.
4. Place slotted masses on the trolley. Connect the trolley via a light string over a smooth pulley to a weight hanger hanging off the edge of the bench.
5. Release the trolley from rest from the same starting line each time. The data logger measures the initial velocity \(u\) at the first light gate, final velocity \(v\) at the second light gate, and the time taken \(t\) between them, calculating acceleration using \(a = \frac{v - u}{t}\).
6. Crucial Step: To increase the pulling force \(F\), transfer a mass from the trolley to the hanger. Do not add external masses, because the total mass of the system (trolley + hanger + masses) must remain strictly constant!

Method: Investigating Acceleration vs Mass (Force Kept Constant)

1. Keep the hanging mass on the hanger constant (this ensures the accelerating force \(F\) does not change).
2. Increase the mass of the trolley by adding slotted masses directly onto the trolley.
3. Record the acceleration for each added mass using the light gates and data logger.
4. Repeat three times for each mass setting and calculate a mean.

Expected Results and Graphs

• Force vs Acceleration: A graph of acceleration (\(y\)-axis) against accelerating force (\(x\)-axis) produces a straight line through the origin. This proves that acceleration is directly proportional to resultant force (\(a \propto F\)).
• Mass vs Acceleration: A graph of acceleration (\(y\)-axis) against total mass (\(x\)-axis) shows that acceleration decreases as mass increases (inversely proportional: \(a \propto \frac{1}{m}\)).

Sources of Error and Practical Tips

• Friction: Friction between the wheels and ramp slows the trolley. Compensate by slightly elevating the runway so the component of gravity down the slope balances friction.
• Reaction Time: Using light gates eliminates human reaction time errors that would occur if using a manual stopwatch.
• Mass Transfer: A very common exam trap! If you take masses from a box and add them only to the hanger, you have changed both force and total mass. You must transfer masses directly from the trolley to the hanger to keep total system mass constant.

Key Takeaway: Acceleration is directly proportional to resultant force and inversely proportional to mass (\(F = m \times a\)). Always use light gates for high precision and transfer masses between trolley and hanger to keep total mass fixed.

2. Core Practical 14.3: Investigating Densities of Solids and Liquids

Aim of the Experiment

To determine the density of regular solids, irregular solids, and liquids using mass and volume measurements, applying the equation:

\(\rho = \frac{m}{V}\)

where \(\rho\) is density in kilograms per cubic metre (\(\text{kg/m}^3\)) or grams per cubic centimetre (\(\text{g/cm}^3\)), \(m\) is mass in kilograms (\(\text{kg}\)) or grams (\(\text{g}\)), and \(V\) is volume in cubic metres (\(\text{m}^3\)) or cubic centimetres (\(\text{cm}^3\)).

Method 1: Regular Solid (e.g., a rectangular block)

1. Measure the mass \(m\) of the block using a top-pan digital balance (zero the balance before use).
2. Measure the length, width, and height using a ruler (or callipers for smaller objects).
3. Calculate the volume: \(V = \text{length} \times \text{width} \times \text{height}\).
4. Substitute mass and volume into \(\rho = \frac{m}{V}\).

Method 2: Irregular Solid (Displacement Method)

1. Measure the mass \(m\) of the irregular solid on a digital balance.
2. Fill a eureka can (displacement can) with water until it reaches just below the spout, allowing excess water to drain out into a waste beaker.
3. Place an empty, dry measuring cylinder beneath the spout.
4. Gently lower the solid into the can using a thin thread (do not drop it in, as splashing loses water and leads to an incorrect volume reading).
5. Collect the displaced water in the measuring cylinder. The volume of displaced water equals the volume \(V\) of the solid.
6. Calculate density using \(\rho = \frac{m}{V}\).

Method 3: Liquids

1. Place an empty, clean measuring cylinder on a digital balance and press the tare (zero) button (or record the empty cylinder's mass).
2. Pour a known volume of liquid into the measuring cylinder (e.g., \(50\ \text{cm}^3\)).
3. Read the volume \(V\) from the scale at eye level from the bottom of the meniscus.
4. Read the mass \(m\) of the liquid directly from the balance (or subtract the empty cylinder mass from the total mass).
5. Calculate \(\rho = \frac{m}{V}\). Repeat with different volumes and determine an average density.

Sources of Error and Precision

• Parallax Error: When reading the measuring cylinder, look straight at the liquid level at eye level, aligned with the bottom of the curved meniscus.
• Zero Error: Ensure the digital balance reads \(0.0\ \text{g}\) before placing items on it.
• Water Droplets: Make sure no water splashes out of the eureka can, and ensure the outside of the can is dry.

Key Takeaway: Density is mass divided by volume. Use direct measurements and geometry for regular solids, water displacement for irregular solids, and a tared balance with a measuring cylinder for liquids.

3. Core Practical 14.11: Investigating the Properties of Water

Part A: Determining the Specific Heat Capacity of Water

Scientific Principle

Specific heat capacity (\(c\)) is the energy required to raise the temperature of \(1\ \text{kg}\) of a substance by \(1\ ^\circ\text{C}\). It is governed by the equation:

\(\Delta Q = m \times c \times \Delta\theta\)

where \(\Delta Q\) is the change in thermal energy in joules (\(\text{J}\)), \(m\) is mass in \(\text{kg}\), \(c\) is specific heat capacity in \(\text{J/(kg}\ ^\circ\text{C)}\), and \(\Delta\theta\) is the temperature change in \(^\circ\text{C}\).

Apparatus

• Insulated beaker or calorimeter with a lid
• Immersion heater
• Thermometer or digital temperature sensor
• Power supply, ammeter, voltmeter, and stopwatch (or a joulemeter)
• Digital balance

Method

1. Place the empty insulated beaker on a balance, zero it, and add water (e.g., \(200\ \text{g} = 0.2\ \text{kg}\)). Record this mass \(m\).
2. Place the immersion heater fully into the water and insert the thermometer.
3. Place a lid on the beaker to reduce thermal energy loss to the air.
4. Record the initial temperature of the water.
5. Switch on the power supply and start the stopwatch. Record the current \(I\) from the ammeter and potential difference \(V\) from the voltmeter.
6. Heat the water for a set time \(t\) (e.g., \(600\ \text{s}\)), gently stirring occasionally to ensure even temperature distribution.
7. Switch off the heater, observe the thermometer, and record the highest maximum temperature reached. Calculate \(\Delta\theta = \theta_{\text{final}} - \theta_{\text{initial}}\).
8. Calculate electrical energy supplied using: \(E = I \times V \times t\).
9. Assuming all electrical energy transfers to thermal energy (\(\Delta Q = E\)), calculate \(c\):
\(c = \frac{\Delta Q}{m \times \Delta\theta}\)

Evaluation and Systematic Errors

• Calculated value is too high: The experimental value of \(c\) for water is almost always higher than the accepted textbook value. Why? Some thermal energy escapes to the surroundings or heats the beaker and heater itself. Therefore, the actual \(\Delta\theta\) is smaller than it should be, making \(c = \frac{\Delta Q}{m \times \Delta\theta}\) appear larger.
• Improvements: Use an insulating jacket (like polystyrene), place a lid on the container, and ensure the immersion heater is fully submerged.

Part B: Temperature-Time Graph for Melting Ice

Method and Principle

1. Place crushed ice into a beaker and insert a thermometer.
2. Record the temperature of the ice at start time \(t = 0\ \text{s}\).
3. Heat the beaker very gently using a low flame (or allow it to warm slowly at room temperature), stirring constantly.
4. Record the temperature every \(30\) or \(60\) seconds until all the ice has melted and the water begins to warm.

Interpreting the Graph

• The Plateau: While the ice is melting, the temperature remains constant at \(0\ ^\circ\text{C}\), producing a horizontal plateau on your temperature-time graph.
• Why? Thermal energy supplied is not increasing the kinetic energy of the particles. Instead, it is being used to overcome and break intermolecular bonds during the change of state from solid to liquid. This energy is the specific latent heat of fusion (\(Q = m \times L\)).
• Once all the ice has melted into liquid water, continued heating causes the temperature to rise again.

Key Takeaway: During temperature changes, use \(\Delta Q = m \times c \times \Delta\theta\). Insulation prevents heat loss that inflates the calculated specific heat capacity. During a change of state (melting ice at \(0\ ^\circ\text{C}\)), temperature remains flat because energy is breaking bonds, not raising kinetic energy.

4. Core Practical 15.6: Extension and Work Done on a Spring

Aim of the Experiment

To investigate the relationship between force and extension for a spring, verify Hooke's Law, determine the spring constant (\(k\)), and calculate the work done in stretching the spring.

Key Equations

• Force exerted by a spring: \(F = k \times x\)
• Energy transferred in stretching (work done): \(E = \frac{1}{2} \times k \times x^2\)

where \(F\) is force in newtons (\(\text{N}\)), \(k\) is spring constant in newtons per metre (\(\text{N/m}\)), \(x\) is extension in metres (\(\text{m}\)), and \(E\) is work done in joules (\(\text{J}\)).

Apparatus

• Clamp stand, boss, and clamp
• Steel helical spring
• Metre ruler secured vertically
• Fiducial marker (pointer attached to bottom of spring)
• Slotted mass hanger and masses (e.g., \(100\ \text{g}\) each, providing weight \(W = m \times g\))

Method

1. Set up the clamp stand with the ruler clamped vertically next to the spring.
2. Attach a horizontal pointer (fiducial marker) to the bottom of the unstretched spring.
3. Record the initial position of the pointer on the ruler (unstretched length \(l_0\)). Ensure your eye is level with the pointer to avoid parallax error.
4. Hang a \(100\ \text{g}\) mass hanger from the spring. The pulling force is its weight (\(W = m \times g = 0.1\ \text{kg} \times 10\ \text{N/kg} = 1.0\ \text{N}\)).
5. Record the new pointer position \(l\).
6. Calculate extension: \(x = l - l_0\).
7. Add further masses one at a time (e.g., up to \(600\ \text{g}\)), recording the new position and calculating total extension for each load.
8. Unload the masses one by one to verify whether the spring returns to its original length (checking for elastic distortion).

Graph and Data Analysis

• Plot a graph of Force (\(F\)) on the \(y\)-axis against Extension (\(x\)) on the \(x\)-axis.
• Linear Region: The line begins straight and passes through the origin. This straight section obeys Hooke's Law: force is directly proportional to extension (\(F \propto x\)). The gradient of this straight line is equal to the spring constant (\(k\)):
\(\text{Gradient} = \frac{\Delta F}{\Delta x} = k\)
• Limit of Proportionality: The point where the graph starts to curve. Beyond this point, the spring exhibits inelastic (plastic) distortion and will not return to its original length when unloaded.
• Work Done (Energy Transferred): The work done in stretching the spring is equal to the area under the force-extension graph. For the linear region, this triangle has an area of:
\(\text{Area} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times x \times F = \frac{1}{2} \times k \times x^2\)

Common Errors and Precautions

• Measuring length instead of extension: A classic mistake! Extension is the change in length (\(x = l - l_0\)), never just the total length.
• Unit Conversions: Ruler measurements are usually in centimetres (\(\text{cm}\)) or millimetres (\(\text{mm}\)). Always convert to metres (\(\text{m}\)) before calculating \(k\) or energy in joules.
• Parallax Error: Avoid misreading the ruler by keeping your eye line perpendicular to the scale, using a set square or horizontal pointer.

Key Takeaway: Force is proportional to extension up to the limit of proportionality (\(F = k \times x\)). The gradient of a force-extension graph gives the spring constant \(k\), and the area underneath equals the work done / elastic energy stored (\(E = \frac{1}{2} \times k \times x^2\)).

Quick Reference Summary Table

• 2.19 Trolley Acceleration: Equation: \(F = m \times a\). Control: move masses between trolley and hanger to keep total system mass constant. Improve: use light gates and compensate runway for friction.
• 14.3 Density: Equation: \(\rho = \frac{m}{V}\). Control: tare balance, read meniscus at eye level. Technique: eureka can displacement for irregular solids.
• 14.11 Thermal Properties: Equations: \(\Delta Q = m \times c \times \Delta\theta\) and \(Q = m \times L\). Control: insulate and add a lid to prevent thermal loss. Insight: flat plateau on graph means latent heat is breaking bonds.
• 15.6 Spring Extension: Equations: \(F = k \times x\) and \(E = \frac{1}{2} \times k \times x^2\). Control: read extension (\(l - l_0\)) using a fiducial marker to avoid parallax. Insight: gradient is \(k\), area under line is work done.