Density, Upthrust & Viscous Drag (Edexcel AS Physics): Exam Questions

A student investigated the viscosity of olive oil at different temperatures using a steel sphere of radius $r$.

Describe how the student can make measurements of the steel sphere to determine its radius accurately.

Explain how the student can ensure that Stokes' law will apply to the steel sphere as it falls through the olive oil.

The student dropped the steel sphere into a tall cylinder of olive oil, as shown, and timed the sphere as it fell through the oil at terminal velocity.

The student placed two rubber bands around the cylinder and started a stopwatch when the sphere passed the first band and stopped it when the sphere passed the second band.

The student recorded the time $t$ for the ball to fall through a distance of $21.0\text{ cm}$ and repeated this for three different temperatures. They calculated the viscosity $\eta$ at each temperature using the formula

$\eta =\frac{2r^{2}g\left({\rho }_s-{\rho }_o\right)}{9v}$

radius of steel sphere $r=2.2\text{ mm}$
density of steel ${\rho }_s=7800{\text{ kg m}}^{-3}$
density of olive oil at 20 °C ${\rho }_o=920{\text{ kg m}}^{-3}$

Their results are shown in the table.

The student concluded that the viscosity of olive oil decreases linearly with temperature.

Criticise the student's investigation and conclusion.

A student determines the viscosity of an engine oil at room temperature using the falling-ball method.

The student releases a small steel ball from rest at the surface of the oil in a tall tube, as shown.

Sketch a graph to show how the velocity of the ball varies with time, from the instant of release until after the ball reaches terminal velocity.

Describe how the student obtains an accurate value for the terminal velocity of the ball.

Explain why the temperature of the oil must be kept constant during the experiment.

The ball has a diameter of $3.0\text{mm}$. The ball falls a distance of $0.240\text{m}$ in a time of $1.6\text{s}$ while travelling at terminal velocity.

density of steel $=7800{\text{kg m}}^{-3}$

density of the oil $=900{\text{kg m}}^{-3}$

Calculate the viscosity of the oil.