Physics practical notes

Calculation D.P. rule Whenever calculating two values that only involve addition and subtraction, the calculated value adopts the least d.p., with a minimum of 0d.p. S.F. rule Any calculation that involves operators other than addition and subtraction, the calculated value adopts the least s.f., with a minimum of 2s.f. Graphical analysis Plot against , based on the given equation and determine the relationship of the graph. 𝑌 𝑋 Proportional relationship When two quantities are directly or inversely proportional to each other. 1. The graph is a straight line 2. Passes through the origin (0,0) Linear relationship When two quantities are linearly related. 1. The graph is a straight line. Non-linear relationship Two quantities create a graph that is curved. 𝑌 = 𝑘𝑋 𝑌 = 𝑚𝑋 + 𝐶 𝑌 = 𝑓 ( 𝑋 ) Constant relationship When two quantities are independent of each other, the graph produces a straight horizontal line. Note: Some graphs are expected to pass through the origin based on the physical relationship between the variables. - For example, if the dependent variable represents the change caused by a limiting reactant, adding 0 volume of the reactant should produce 0 change in the system. Therefore, the graph should pass through the origin . ( 0 , 0 ) 𝑌 = 𝑘 Quantity Algebra: both the numerical magnitude and unit of a quantity are substituted for its symbol in the equation. Number Algebra: only the numerical magnitude of a quantity is substituted for its symbol in the equation, converted to the usual units by applying the appropriate multiplying factor. Errors and uncertainty Systemic error Constant deviations of the readings in one direction from the true value. - Zero error - Reaction time - Wrongly calibrated scale Systematic errors can be reduced by calibration curves and control experiments. Random error Measurements are scattered around a mean value. - Reading a scale by interpolation - Timing oscillations without a reference marker - Taking readings of a quantity that varies with time. - Parallax error. Random error can be mitigated by averaging the values, repeating the experiment or by drawing a graph. Accuracy: how close a measurement is to the actual value - Note: accuracy has a 10% range from the true value. Precision: how close the measurements are to each other, or to a mean value

Uncertainty is a range of values in which a measurement can fall. - Uncertainty of a digital equipment is one unit of the smallest scale of the instrument. - Uncertainty of an analogue instrument is half the smallest division of the scale. 𝑀 1 = 𝑀 0 ± δ 𝑀 Average of values, σ 𝑚 = ∑ 𝑛 𝑥 𝑛 - σ 𝑚 1 = σ 𝑚 ± 𝑚𝑎𝑥 ( 𝑥 ) − 𝑚𝑖𝑛 ( 𝑥 ) 2 - Note: when calculating the mean of values, it follows the d.p. rule Absolute uncertainty, δPercentage uncertainty, 𝑃 𝑀 = δ 𝑀 𝑀 0 × 100%Addition or subtraction of uncertainties, ( 𝐴 0 + 𝐵 0 ) ± ( δ 𝐴 + δ 𝐵 )Multiplication or division of uncertainties, 𝐴 0 𝐵 0 ± 𝐴 0 𝐵 0 ( 𝑃 𝐴 + 𝑃 𝐵 )Power or root of uncertainties, 𝐴 0 𝐾 𝐵 0 𝐽 ± 𝐴 0 𝐾 𝐵 0 𝐽 ( | 𝐾 | 𝑃 𝐴 + | 𝐽 | 𝑃 𝐵 )Note: d.p. Of both must be the same. Increasing accuracy When measuring the diameter of an object, take repeated readings at different positions across the diameter, finding the average of all the readings. When measuring the time taken, take repeated readings, finding the average of all the readings. Precision of instrument For digital measuring instruments, the measurement uncertainty is typically ±1 in the last displayed digit. Therefore, record all the digits shown by the display. - Example: If a digital micrometre displays 12.3456 mm, record 12.3456 mm ± 0.0001 mm. Do not round it to 12.346 mm. - Includes: Digital multimeter, digital micrometre screw gauge, digital vernier callipers. For analogue measuring instruments with discrete scale divisions, the measurement uncertainty is typically ±½ of the smallest scale division. - Example: A metre rule has the smallest division of 0.1 cm (1 mm), so the uncertainty is ±0.05 cm (±0.5 mm). Measurements are therefore estimated to the nearest 0.05 cm. - Includes: voltmeter, ammeter, thermometer, ruler, vernier callipers, micrometre screw gauge. Systematic error A consistent, repeatable deviation in one direction. Procedural error An issue with the design of the experiment. Using tools Micrometre screw gauge Sleeve (Pitch) Scale: The sleeve (pitch) scale measures the length to the nearest 0.5 mm. Each division on the sleeve represents 0.5 mm. Read the last visible marking on the sleeve before the edge of the thimble. Thimble (Circular) Scale: The thimble (circular) scale measures to the nearest 0.01 mm. Each division on the thimble represents 0.01 mm. Read the value on the thimble that aligns with the reference line on the sleeve.

Final Reading: The measurement is obtained by adding the sleeve (pitch) scale reading and the thimble (circular) scale reading. Vernier Calipers Main Scale: The main scale measures the length to the nearest 1 mm (0.1 cm). Read the value immediately to the left of the Vernier zero. Vernier Scale: The Vernier scale measures the fractional part of the reading to the nearest 0.1 mm (0.01 cm). Identify the Vernier division that aligns exactly with a division on the main scale. Multiply the Vernier division number by 0.1 mm to obtain the Vernier reading. Final Reading: Add the main scale reading and the Vernier scale reading to obtain the total measurement. Method for planning experiments Aim → Variables → Apparatus → Method → Calculation → Graph → Accuracy → Errors → Assumptions Improving the experiment Improvement → Mechanism → Effect on measurement Experiments Independent variable: the variable you can directly change - Indirectly changing variables are resistance, current, voltage, etc. These changes are affected by another change, like a rheostat. Dependent variable: the variable that changes as a result of changing the independent variable. - Otherwise, the value you are reading. Control variable: conditions of the system that should remain constant. Measuring density Volume

Setting up: 1. Add the liquid to a displacement can, which leads to a measuring cylinder. 2. Tie the object tightly to a rope, and attach the end of the rope to a retort stand. Experimental procedure(: 1. Slowly release the rope on the retort stand so that the object slowly descends into the liquid. 2. Once the object is fully submerged, measure the volume of the liquid displaced into the measuring cylinder. Record this volume as . 𝑉3. Repeat steps 1 to 2 for new values of , ensuring that the 𝑉object is dried afterwards and the liquid is refilled. 4. Calculate the average volume by taking the average of . 𝑉 Accuracy: 1. Volume of liquid collected - Use a liquid with low viscosity. - This allows the displaced liquid to flow quickly and completely into the measuring cylinder, reducing the amount of liquid retained in the displacement c