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Experimental Programme - Internal Assessment (Scientific Investigation)

Grade 12IBPhysics

Review the key concepts, formulae, and examples before starting your quiz.

🔑Concepts

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The Research Question (RQ) must be sharply focused and clearly state the independent variable (IVIV) and the dependent variable (DVDV). It often takes the form: 'How does IVIV affect DVDV when controlled variables are kept constant?'

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Independent variables are systematically manipulated, while dependent variables are measured. Control variables must be identified and their monitoring/maintenance described to ensure a 'fair test'.

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Uncertainties are categorized as random or systematic. Random errors affect the precision of measurements and can be reduced by repeating trials. Systematic errors (e.g., zero offset) affect the accuracy and shift results in a specific direction.

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Data processing involves calculating the mean of repeated trials and determining the absolute uncertainty in the DVDV using Δy=ymax−ymin2\Delta y = \frac{y_{max} - y_{min}}{2}.

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Linearization is the process of transforming a non-linear relationship (e.g., y=axny = ax^n) into a linear form (e.g., log⁡(y)=nlog⁡(x)+log⁡(a)\log(y) = n\log(x) + \log(a)) to determine physical constants from the gradient or intercept.

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The 'Line of Best Fit' must pass through all error bars. To find the uncertainty in the gradient mm, students should draw the 'Maximum Gradient' and 'Minimum Gradient' lines that still pass through the error bars.

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Evaluation involves assessing the methodology, identifying specific sources of error (not just 'human error'), and suggesting realistic improvements to increase the reliability and validity of the data.

📐Formulae

Percentage Uncertainty=Absolute Uncertainty (Δx)Measured Value (x)×100%\text{Percentage Uncertainty} = \frac{\text{Absolute Uncertainty (}\Delta x\text{)}}{\text{Measured Value (}x\text{)}} \times 100\%

Addition/Subtraction: If y=a±b, then Δy=Δa+Δb\text{Addition/Subtraction: If } y = a \pm b, \text{ then } \Delta y = \Delta a + \Delta b

Multiplication/Division: If y=a×bc, then Δyy=Δaa+Δbb+Δcc\text{Multiplication/Division: If } y = \frac{a \times b}{c}, \text{ then } \frac{\Delta y}{y} = \frac{\Delta a}{a} + \frac{\Delta b}{b} + \frac{\Delta c}{c}

Power Rule: If y=an, then Δyy=∣n∣Δaa\text{Power Rule: If } y = a^n, \text{ then } \frac{\Delta y}{y} = |n| \frac{\Delta a}{a}

Δm=mmax−mmin2\Delta m = \frac{m_{max} - m_{min}}{2}

Δc=cmax−cmin2\Delta c = \frac{c_{max} - c_{min}}{2}

💡Examples

Problem 1:

A student measures the mass of a metal sphere as m=50.0±0.1 gm = 50.0 \pm 0.1\text{ g} and its volume as V=10.0±0.5 cm3V = 10.0 \pm 0.5\text{ cm}^3. Calculate the density ρ\rho and its absolute uncertainty Δρ\Delta \rho.

Solution:

  1. Calculate density: ρ=mV=50.010.0=5.0 g cm−3\rho = \frac{m}{V} = \frac{50.0}{10.0} = 5.0\text{ g cm}^{-3}.
  2. Calculate fractional uncertainties: Δmm=0.150.0=0.002\frac{\Delta m}{m} = \frac{0.1}{50.0} = 0.002; ΔVV=0.510.0=0.05\frac{\Delta V}{V} = \frac{0.5}{10.0} = 0.05.
  3. Add fractional uncertainties: Δρρ=0.002+0.05=0.052\frac{\Delta \rho}{\rho} = 0.002 + 0.05 = 0.052.
  4. Find absolute uncertainty: Δρ=0.052×5.0=0.26 g cm−3\Delta \rho = 0.052 \times 5.0 = 0.26\text{ g cm}^{-3}.
  5. Final result: ρ=5.0±0.3 g cm−3\rho = 5.0 \pm 0.3\text{ g cm}^{-3} (rounded to 1 sig. fig. of uncertainty).

Explanation:

When dividing two quantities, the fractional (or percentage) uncertainties are added to find the total fractional uncertainty of the result.

Problem 2:

To find the acceleration due to gravity gg using a pendulum of length ll, the student uses the formula T=2πlgT = 2\pi\sqrt{\frac{l}{g}}. How should the data be linearized to find gg from a graph?

Solution:

Square both sides of the equation: T2=4π2glT^2 = \frac{4\pi^2}{g}l. Comparing this to y=mx+cy = mx + c, we plot T2T^2 on the y-axis and ll on the x-axis. The gradient mm of the line will be m=4π2gm = \frac{4\pi^2}{g}. Therefore, g=4π2mg = \frac{4\pi^2}{m}.

Explanation:

Linearizing the data allows the use of a line of best fit to average out random errors and provides a straightforward way to calculate a physical constant (gg) from the gradient.

Internal Assessment (Scientific Investigation) Revision - Grade 12 Physics IB