IB Physics HL S2.2 Collecting and Processing Data Topic Practice

A student determines the resistivity $\rho$ of a metal that is in the form of a cylindrical wire. The student makes the following measurements:

Show that the mean diameter of the wire is about 0.2 mm .

A student attaches one end of a copper wire to an oscillator operating at a fixed frequency. The other end of the wire passes over a pulley to weights that hang vertically. The first harmonic standing wave is established by using the slider to change the length of the wire. The procedure is repeated for different weights.

The mass m of the weights and the wavelength $\lambda$ of the wave are related by

where $\mu$ is a constant, f is the frequency of the wave and $g=9.8 \mathrm{~ms}^{-2}$.

The graph shows the data obtained by the student, plotted to show the variation of m with $\lambda^{2}$.

Identify the evidence for a systematic error in the data.

A student investigates whether the Stefan-Boltzmann law, $L=4 \pi \sigma R^{2} T^{4}$, applies to stars.
L= luminosity of the star, in W
$\sigma=$ Stefan-Boltzmann constant
R= radius of the star, in m
T= surface temperature of the star, in K
To verify the law, they obtain values from databases and manipulate the data as shown.

Complete the table with the missing values for Polaris B.

The student plots the variation with $\log T$ of $\log \left(\frac{L}{R^{2}}\right)$ and draws the line of best fit.

The student uses a GDC (graphical display calculator) to determine the equation of the line of best fit as y=3.99 x-6.15.