Edexcel A-Level Physics A2 C 3 11 Testing Laws with Logarithmic Plots Questions

Review testing laws with logarithmic plots in Edexcel A-Level Physics through power-law gradients, exponential decay and processed log data.

Exam points

transform a power-law relationship into a straight-line log plot and use its gradient
linearise exponential decay data so the gradient gives the decay constant or related parameter
process logarithmic table columns before plotting and interpreting the tested physical law

[Maximum number: 2]

A student investigated the damping of a rotational pendulum using the apparatus shown.

Figure for Question Edexcel A-Level Physics A2 C 3 11 Testing Laws with Logarithmic Plots Questions question 1 — Edexcel A-Level Physics A2

When the metal rod is rotated through an angle and released, the rod performs angular oscillations about a vertical axis through the wire. The plastic sheets dampen the oscillations as they move through the air.

The relationship between the maximum displacement angle $\theta$ and number of oscillations n is given by

$\theta=\theta_0e^{-\lambda n},$

where $\theta_0$ is the initial displacement angle and $\lambda$ is a constant.

Explain why a graph of $\ln\theta$ against n could be used to determine a value for $\lambda$ .

Taking natural logarithms gives

$\ln\theta=\ln\theta_0-\lambda n.$

This has the form y=c+mx, so a graph of $\ln\theta$ against n is linear with gradient $-\lambda$ .

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Edexcel A-Level Physics A2 C 3 11 Testing Laws with Logarithmic Plots Questions question 1