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.

A spherical soap bubble is made of a thin film of soapy water. The bubble has an internal air pressure $P_{\mathrm{i}}$ and is formed in air of constant pressure $P_{\mathrm{o}}$. The theoretical prediction for the variation of ( $P_{\mathrm{i}}-P_{\mathrm{o}}$ ) is given by the equation

where $\gamma$ is a constant for the thin film and R is the radius of the bubble.
Data for ( $P_{\mathrm{i}}-P_{\mathrm{o}}$ ) and R were collected under controlled conditions and plotted as a graph showing the variation of ( $P_{\mathrm{i}}-P_{\mathrm{o}}$ ) with $\frac{1}{R}$.

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 $g=9.8 \mathrm{~ms}^{-2}$.

In an experiment to measure the acceleration of free fall a student ties two different blocks of masses $m_{1}$ and $m_{2}$ to the ends of a string that passes over a frictionless pulley.

The student calculates the acceleration a of the blocks by measuring the time taken by the heavier mass to fall through a given distance. Their theory predicts that $a=g \frac{m_{1}-m_{2}}{m_{1}+m_{2}}$ and this can be re-arranged to give $g=a \frac{m_{1}+m_{2}}{m_{1}-m_{2}}$.

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 $g=9.8 \mathrm{~ms}^{-2}$.

Ion-thrust engines can power spacecraft. In this type of engine, ions are created in a chamber and expelled from the spacecraft. The spacecraft is in outer space when the propulsion system is turned on. The spacecraft starts from rest.

The mass of ions ejected each second is $6.6 \times 10^{-6} \mathrm{~kg}$ and the speed of each ion is $5.2 \times 10^{4} \mathrm{~m} \mathrm{~s}^{-1}$. The initial total mass of the spacecraft and its fuel is 740 kg . Assume that the ions travel away from the spacecraft parallel to its direction of motion.

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.

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.

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.

Data analysis question.

Connie and Sophie investigate the effect of colour on heat absorption. They make grey paint by mixing black and white paint in different ratios. Five identical tin cans are painted in five different shades of grey.

Connie and Sophie put an equal amount of water at the same initial temperature into each can. They leave the cans under a heat lamp at equal distances from the lamp. They measure the temperature increase of the water, T, in each can after one hour.