Measurement of Physical Quantities and Experimental Errors for SS 1

Quantities and Measurements

Performance Objectives

By the end of the lesson, students should be able to:

1. identify various measurable physical quantities and their units (length, mass, time, temperature, etc.);
2. measure quantities including length, mass, time, temperature, and charge using specific instruments;

Introduction to Physical Quantities and Units

Physics is an experimental science that relies on observations and measurements. To describe the world around us accurately, we need to measure various aspects of objects and phenomena. These measurable aspects are called physical quantities.

A physical quantity is a property of a material or system that can be quantified by measurement.

Examples of physical quantities include length, mass, time, temperature, and electric charge. Each physical quantity has a standard unit for its measurement, which allows scientists and engineers worldwide to communicate measurements consistently.

The International System of Units (SI) provides a standard set of units for physical quantities. Using these standard units ensures that measurements are understood universally.

Common physical quantities and their SI units include:

1. Length: Metre (m)
2. Mass: Kilogram (kg)
3. Time: Second (s)
4. Temperature: Kelvin (K) (though Celsius, °C, is also widely used)
5. Electric Current: Ampere (A) (related to charge)
6. Electric Charge: Coulomb (C)

Measurement of Time

Time is a fundamental physical quantity that describes the duration of events or the interval between them. Measuring time accurately is essential in many scientific experiments and daily activities.

Instruments for Measuring Time

The common instruments used for measuring time in physics experiments are the stopwatch and the stop clock.

1. Stopwatch: A stopwatch is a handheld timepiece designed to measure the amount of time that elapses from a particular start time to a stop time. It is commonly used for measuring short durations, such as the time taken for a runner to complete a race or the period of a pendulum’s swing.

2. Stop Clock: A stop clock is similar to a stopwatch but is often larger and designed for tabletop use in laboratories. It typically has a large dial with hands, making it easy to read from a distance. It also measures elapsed time from start to stop.

How to Measure Time Using a Stopwatch or Stop Clock

Measuring time accurately requires careful handling of the instrument and good observation skills. The procedure involves the following steps:

1. Reset the Instrument: Before starting any measurement, ensure the stopwatch or stop clock is reset to zero. For digital stopwatches, press the reset button. For analog stop clocks, press the reset button to bring the hands back to the zero mark.
2. Start Timing: As the event begins, press the start button simultaneously. For example, if measuring the period of a pendulum, start the clock as the pendulum passes a specific point.
3. Stop Timing: As the event ends, press the stop button immediately. Try to stop the clock at the exact moment the event concludes.
4. Read the Time: Read the elapsed time displayed on the stopwatch or stop clock. For analog clocks, read the position of the hands on the dial. For digital ones, read the numerical display.
5. Repeat Measurement: For greater accuracy, it is often recommended to repeat the measurement several times and calculate the average time. This helps to minimise random errors.

Measurement of Length

Length is the measurement of distance between two points. It is a fundamental quantity used to describe the size of objects or the extent of space. Different instruments are used to measure length depending on the required precision and the size of the object.

Instruments for Measuring Length

Various instruments are used to measure length, each suited for different ranges and levels of precision:

1. Ruler: A ruler is a flat, straight strip, usually made of wood, plastic, or metal, marked with units of length (centimetres and millimetres, or inches). It is used for measuring short lengths, typically up to 30 cm, and is common in schools and offices.

2. Meter Rule: A meter rule is similar to a ruler but is typically one metre (100 cm) long. It is used for measuring longer lengths than a standard ruler, such as the dimensions of a table or the height of a person.

3. Tape Rule (Measuring Tape): A tape rule is a flexible strip of cloth, plastic, or metal, marked with units of length, that can be rolled up. It is ideal for measuring curved surfaces, long distances, or around objects, such as waist measurements or room dimensions. Tape rules can be several metres long.

4. Vernier Callipers: Vernier callipers are precision instruments used for measuring internal and external diameters, as well as depths, with greater accuracy than a ruler. They can measure lengths to an accuracy of 0.01 cm or 0.1 mm.

   The main parts of a Vernier calliper include the main scale, Vernier scale, external jaws, internal jaws, and a depth rod.

   Reading Vernier Callipers:

   1. Main Scale Reading (MSR): Read the value on the main scale immediately before the zero mark of the Vernier scale.
   2. Vernier Scale Reading (VSR): Find the mark on the Vernier scale that perfectly aligns or coincides with any mark on the main scale. Multiply this coinciding mark by the least count of the Vernier calliper (usually 0.01 cm or 0.1 mm).
   3. Total Reading: Add the Main Scale Reading and the Vernier Scale Reading: Total Reading = MSR + VSR.

   Zero Error: Vernier callipers can have a zero error if the zero mark of the Vernier scale does not coincide with the zero mark of the main scale when the jaws are closed.

   1. Positive Zero Error: If the Vernier zero mark is to the right of the main scale zero mark. The error is read like a normal VSR when jaws are closed.
   2. Negative Zero Error: If the Vernier zero mark is to the left of the main scale zero mark. The error is calculated as (Total divisions on Vernier scale – coinciding division) × Least Count.
   3. Corrected Reading: Actual Length = Total Reading – Zero Error (with its sign).

5. Micrometre Screw Gauge: A micrometre screw gauge is an even more precise instrument used for measuring very small lengths, such as the thickness of a wire or a sheet of paper, to an accuracy of 0.01 mm or 0.001 cm.

   Its main parts include the main scale (sleeve), thimble scale, spindle, anvil, frame, and ratchet.

   Reading a Micrometre Screw Gauge:

   1. Main Scale Reading (MSR): Read the value on the main scale (sleeve) that is visible just before the edge of the thimble. Note both the millimetre and half-millimetre marks if visible.
   2. Thimble Scale Reading (TSR): Find the mark on the thimble scale that aligns with the main line of the main scale. Multiply this reading by the least count of the micrometre screw gauge (usually 0.01 mm).
   3. Total Reading: Add the Main Scale Reading and the Thimble Scale Reading: Total Reading = MSR + TSR.

   Zero Error: Similar to Vernier callipers, a micrometre screw gauge can have a zero error.

   1. Positive Zero Error: If the zero mark of the thimble scale is below the main line when the anvil and spindle are closed.
   2. Negative Zero Error: If the zero mark of the thimble scale is above the main line when the anvil and spindle are closed.
   3. Corrected Reading: Actual Length = Total Reading – Zero Error (with its sign).

How to Measure Length Using Specific Instruments

The method of measurement depends on the instrument and the object being measured.

1. Using a Ruler/Meter Rule/Tape Rule:
   1. Place the instrument alongside the object to be measured, ensuring the zero mark aligns with one end of the object.
   2. Read the mark on the scale that aligns with the other end of the object.
   3. For accurate readings, always view the scale perpendicularly to avoid parallax error.
2. Using Vernier Callipers:
   1. Clean the jaws and check for zero error. Record any zero error.
   2. Place the object firmly between the external jaws (for external diameter/length) or internal jaws (for internal diameter). For depth, use the depth rod.
   3. Tighten the thumbscrew gently to hold the object.
   4. Read the Main Scale Reading (MSR) and the Vernier Scale Reading (VSR).
   5. Calculate the total reading and apply the zero correction.
3. Using a Micrometre Screw Gauge:
   1. Clean the anvil and spindle faces and check for zero error. Record any zero error.
   2. Place the object between the anvil and the spindle.
   3. Turn the ratchet knob until it clicks, indicating the object is held with the correct pressure. Do not overtighten.
   4. Read the Main Scale Reading (MSR) and the Thimble Scale Reading (TSR).
   5. Calculate the total reading and apply the zero correction.

Measurement of Mass

Mass is a measure of the amount of matter in an object. It is a fundamental property of an object and is distinct from weight, which is the force of gravity acting on an object. Mass is measured in kilograms (kg) in the SI system.

Instruments for Measuring Mass

Various types of balances and scales are used to measure mass, ranging from simple to highly precise instruments.

1. Beam Balance: A beam balance works on the principle of moments. It compares an unknown mass with known standard masses. When the beam is balanced, the mass of the object is equal to the sum of the standard masses.

2. Spring Balance: A spring balance measures mass by measuring the force (weight) exerted by the object on a spring. The spring stretches in proportion to the applied force (Hooke’s Law), and the scale is calibrated to display mass or weight. It is less accurate than a beam balance for measuring mass because its reading can be affected by gravity variations.

3. Chemical Balance: A chemical balance is a highly sensitive type of beam balance used in laboratories for precise measurement of small masses, often in chemical experiments. They are enclosed in a glass case to prevent air currents from affecting the measurement.

4. Digital Scientific Balances: These are modern electronic balances that provide a direct digital readout of mass. They are highly accurate, easy to use, and commonly found in laboratories, schools, and industries.

5. Modern Digital and Spring Scales: These include various types of scales used in homes, markets, and clinics. Digital scales provide numerical readings, while modern spring scales (like bathroom scales) use springs but often have a dial or digital display. They are generally less precise than laboratory balances.

6. Inertia Balance: An inertia balance measures the inertial mass of an object, which is its resistance to acceleration. It works by oscillating an object and measuring the period of oscillation. The greater the mass, the longer the period of oscillation. It is useful for measuring mass in environments where gravity is absent or variable, such as in space.

How to Measure Mass Using Specific Instruments

1. Using a Beam Balance:
   1. Ensure the balance is level and the pointer is at zero when both pans are empty.
   2. Place the object of unknown mass on one pan.
   3. Place known standard masses on the other pan until the beam is balanced and the pointer returns to zero.
   4. The total mass of the standard weights equals the mass of the object.
2. Using a Spring Balance:
   1. Hold the spring balance vertically by its top hook.
   2. Ensure the pointer is at zero. If not, adjust it if possible, or note the zero error.
   3. Attach the object to be weighed to the bottom hook.
   4. Read the value indicated by the pointer on the scale.
3. Using a Digital Balance:
   1. Place the balance on a stable, level surface.
   2. Turn on the balance and allow it to stabilise.
   3. Press the “Tare” or “Zero” button to set the display to zero if there is a container on the pan.
   4. Place the object directly on the weighing pan.
   5. Read the mass displayed on the screen.

Measurement of Temperature

Temperature is a measure of the degree of hotness or coldness of an object or substance. It indicates the average kinetic energy of the particles within a substance. The SI unit for temperature is Kelvin (K), but Celsius (°C) is commonly used in daily life and many scientific contexts.

Instruments for Measuring Temperature

Different instruments are used to measure temperature, each suited for specific temperature ranges and applications.

1. Liquid-in-Glass Thermometers: These are the most common type of thermometers. They consist of a glass bulb connected to a thin capillary tube, partially filled with a liquid (usually mercury or coloured alcohol). The liquid expands when heated and contracts when cooled, causing its level in the capillary tube to rise or fall, indicating the temperature on a calibrated scale.

2. Digital Thermometers: Digital thermometers use electronic sensors (thermistors or resistance temperature detectors) to measure temperature. They convert the temperature reading into an electrical signal, which is then displayed as a numerical value on a digital screen. They are fast, accurate, and easy to read.

3. Thermocouple: A thermocouple consists of two wires made of different metals, joined at two points (junctions). When there is a temperature difference between the two junctions, a small voltage is generated (Seebeck effect). This voltage is proportional to the temperature difference and can be measured to determine the temperature. Thermocouples are robust and can measure a wide range of temperatures, including very high ones.

4. Pyrometer: A pyrometer is a non-contact thermometer used to measure very high temperatures, typically of hot objects like furnaces or molten metals, by detecting the thermal radiation emitted by the object. It does not need to touch the object, making it suitable for extremely hot or inaccessible surfaces.

How to Measure Temperature Using Specific Instruments

1. Using a Liquid-in-Glass Thermometer:
   1. Hold the thermometer by the top, away from the bulb.
   2. Place the bulb in contact with the substance or area whose temperature is to be measured.
   3. Wait for the liquid column to stop rising or falling, indicating it has reached thermal equilibrium.
   4. Read the temperature by looking at the level of the liquid column against the scale, ensuring your eye is level with the top of the liquid to avoid parallax error.
2. Using a Digital Thermometer:
   1. Turn on the thermometer.
   2. Place the probe or sensor in contact with the substance or area.
   3. Wait for the digital display to stabilise and show the final temperature reading.
3. Using a Thermocouple:
   1. Connect the thermocouple to a suitable measuring device (e.g., a voltmeter or a dedicated temperature reader).
   2. Place the hot junction at the point where the temperature is to be measured.
   3. Keep the cold junction at a known reference temperature (e.g., in an ice bath) or use a device with internal cold junction compensation.
   4. Read the voltage generated, which is then converted to temperature using a calibration table or built-in software.
4. Using a Pyrometer:
   1. Point the pyrometer at the hot object whose temperature is to be measured.
   2. Ensure there are no obstructions between the pyrometer and the object.
   3. Read the temperature displayed on the pyrometer’s screen.

Measurement of Electric Charge

Electric charge is a fundamental property of matter that causes it to experience a force when placed in an electromagnetic field. It can be positive or negative. The SI unit of electric charge is the Coulomb (C).

While directly measuring a static charge quantity can be complex, instruments are used to detect the presence of charge and to measure electric current, which is the rate of flow of charge.

Instruments for Measuring Charge and Current

1. Gold Leaf Electroscope: A gold leaf electroscope is an instrument used to detect the presence and sign of an electric charge on an object. It consists of a metal rod with a metal cap at one end and two thin gold leaves (or aluminium foil leaves) at the other, enclosed in a glass case.

   When a charged object is brought near the cap, or touches it, charge is transferred to the leaves, causing them to diverge (move apart) due to electrostatic repulsion. The degree of divergence gives a qualitative indication of the amount of charge.

2. Ammeter: An ammeter is an instrument used to measure electric current in a circuit. Electric current is defined as the rate of flow of electric charge. The SI unit for electric current is the Ampere (A), where 1 Ampere is equal to 1 Coulomb of charge flowing per second (1 A = 1 C/s).

   Ammeters are connected in series within a circuit to measure the current flowing through that part of the circuit.

How to Use Specific Instruments for Charge and Current

1. Using a Gold Leaf Electroscope:
   1. Ensure the electroscope is discharged (leaves are closed).
   2. Bring a charged object near the metal cap (for induction) or touch the cap with the charged object (for conduction).
   3. Observe the gold leaves. If they diverge, the object is charged. The extent of divergence indicates the relative amount of charge.
   4. To determine the sign of the charge, first charge the electroscope with a known charge (e.g., by rubbing a plastic rod with wool to get a negative charge and touching the cap). Then bring the unknown charged object near the cap. If the leaves diverge further, the unknown charge is the same sign. If they collapse slightly before diverging again, the unknown charge is opposite.
2. Using an Ammeter:
   1. Identify the positive (+) and negative (-) terminals of the ammeter.
   2. Connect the ammeter in series with the component through which the current is to be measured. This means breaking the circuit and inserting the ammeter so that the current flows through it.
   3. Ensure the positive terminal of the ammeter is connected to the positive side of the power source (or where current enters the component), and the negative terminal to the negative side (or where current leaves the component).
   4. Select an appropriate range on the ammeter if it has multiple ranges. Start with the highest range to avoid damaging the instrument.
   5. Read the value indicated by the pointer on the scale (for analog ammeters) or the numerical display (for digital ammeters).