IB Physics HL S1.3 Mathematics Questions

A girl rides a bicycle that is powered by an electric motor. A battery transfers energy to the electric motor. The emf of the battery is 16 V and it can deliver a charge of 43 kC when discharging completely from a full charge.

The maximum speed of the girl on a horizontal road is $7.0 \mathrm{~m} \mathrm{~s}^{-1}$ with energy from the battery alone. The maximum distance that the girl can travel under these conditions is 20 km .

Show that the time taken for the battery to discharge is about $3 \times 10^{3} \mathrm{~s}$.

Two forces, F and G, act on a system.

F is reversed in direction and G is halved.
Which vector correctly represents the new resultant force?

A rod, R , lies perpendicular to a uniform magnetic field B of strength 0.50 T directed into the plane of the page. R is connected to a circuit and the electric current $I_{\mathrm{R}}$ is 2.0 A .

$\quad B$ is removed and a wire Z, carrying a current $I_{Z}$, is placed parallel to R.

Derive the units of $\mu_{0}$ in SI fundamental units.

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 $m_{\text {immersed }}=1.208 \mathrm{~g}$ 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.

They repeat the experiment several times and estimate an average for

They use the equation

where
r= radius of the sphere,
$v_{\mathrm{t}}=$ terminal velocity of the sphere,
$\eta=$ viscosity of the liquid.
The radius r of the sphere is 3.520 mm .

Calculate the viscosity of the liquid and its absolute uncertainty. Ignore uncertainties in the mass, radius and volume of the sphere. Give your answer in the form $\eta \pm \Delta \eta$, to an appropriate number of significant figures, including units.

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 $m_{\text {immersed }}=1.208 \mathrm{~g}$ 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.

To determine the viscosity, they immerse the sphere in the liquid and drop it from rest.
They collect values and plot a graph of the position d of the sphere from the moment they drop it. They verify that the sphere reaches terminal velocity $v_{t}$ after 0.5 s .

Draw the line of best fit on the graph.