IB Physics HL S2.3 Concluding and evaluating Question Bank

A student investigates the oscillation of a horizontal rod hanging at the end of a vertical string. The diagram shows the view from above.

The student starts the rod oscillating and measures the largest displacement for each cycle of the oscillation on the scale and the time at which it occurs. The student begins to take measurements a few seconds after releasing the rod.

The graph shows the variation of displacement x with time t since the release of the rod. The uncertainty for t is negligible.

A group of students is trying to determine the density and the viscosity of a liquid.

To determine the density, they use a balance to read the mass m of a sphere in air and immersed in the liquid.

They use a sphere of volume $V=1.827 \times 10^{-7} \mathrm{~m}^{3}$.
The readings are $m_{\text {air }}=1.427 \mathrm{~g}$ in air and $m_{\text {lmmersed }}=1.208 \mathrm{~g}$ in the liquid.
The readings are different due to buoyancy. The buoyancy force $F_{\mathrm{b}}$ is given by

where V is the volume of the sphere and $\rho$ is the density of the liquid.

Data analysis question.

An experiment is undertaken to investigate the relationship between the temperature of a ball and the height of its first bounce.

A ball is placed in a beaker of water until the ball and the water are at the same temperature. The ball is released from a height of 1.00 m above a bench. The maximum vertical height h from the bottom of the ball above the bench is measured for the first bounce. This procedure is repeated twice and an average $h_{\text {mean }}$ is calculated from the three measurements.

The procedure is repeated for a range of temperatures. The graph shows the variation of $h_{\text {mean }}$ with temperature T.

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 density of a metal sphere is determined using a digital caliper and a mass balance.

The digital caliper is used to measure the diameter D of the sphere by placing the sphere in the jaws of the digital caliper. This reading is shown.

The sphere is then removed and another reading is taken immediately afterwards with the jaws closed.

The air in a kitchen has pressure $1.0 \times 10^{5} \mathrm{~Pa}$ and temperature $22^{\circ} \mathrm{C}$. A refrigerator of internal volume $0.36 \mathrm{~m}^{3}$ is installed in the kitchen.

This question is about change of phase.

An experiment is conducted to measure the specific heat capacity of water. A mass of water is placed in a glass beaker and energy is transferred from an electric heater.

The data collected are:

Mass of water $=(0.250 \pm 0.002) \mathrm{kg}$
Change in temperature of the water $=(14.0 \pm 0.5)^{\circ} \mathrm{C}$
Energy transferred from the electric heater $=(16000 \pm 300) \mathrm{J}$

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.

The circuit shown may be used to measure the internal resistance of a cell.