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ASPhysicsEdexcelExam Questions4. MaterialsDensity, Upthrust & Viscous Drag

Density, Upthrust & Viscous Drag (Edexcel AS Physics)

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Density, Upthrust & Viscous Drag

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Density, Upthrust & Viscous Drag

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1a
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Raindrops of different sizes fall with different terminal velocities through air.

The table shows the measured value of the terminal velocity for raindrops of different sizes.

Raindrop size Drop diameter / mm Terminal velocity / m s-1
small 0.5 2.1
medium 2.0 6.5
large 5.0 9.1

Derive, using Stokes’ law, the following expression for the terminal velocity v of a spherical raindrop in terms of its radius r.

v space equals space fraction numerator 2 g rho r squared over denominator 9 eta end fraction

where rho is the density of rainwater and eta is the viscosity of air.

You should ignore upthrust.

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1b
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Show that the expression given in (a) produces a value of about 800 m s-1 for the terminal velocity of a large raindrop.

rho = 1.0 × 103 kg m-3
eta = 1.8 × 10-5 Pa s

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1c
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Explain whether Stokes’ law is suitable for calculating the terminal velocity of raindrops.

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1a
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Genuine crystal balls are made from clarified quartz rather than glass.

A student was given a small crystal ball and wanted to know whether it was genuine.

The mean diameter of the crystal ball was measured to be 5.06 cm and the mass of the crystal ball was measured to be 175 g.

 

Show that the density of the material of the crystal ball is about 2600 kg m−3.

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1b
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The student measured the diameter of the crystal ball using vernier calipers with a resolution of 0.01 cm.

 

She measured the mass of the crystal ball using a balance with a resolution of 1 g.
 
The table gives the densities of clarified quartz and glass.

Material Density / kg m−3
Clarified quartz 2650
Glass 2590

 

Determine whether the crystal ball was genuine.

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2a
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A student investigated the terminal velocity of steel spheres falling through oil.

The student obtained the following results.

radius of steel sphere = 1.50 mm
volume of steel sphere = 1.41 × 10−8 m3
mass of steel sphere = 1.10 × 10−4 kg
maximum speed of sphere = 0.849 ms−1

The student had the following table.

Type of oil Density at
26°C / kg m−3		 Viscosity at
26 °C / Pa s
Corn 918 0.0447
Hazelnut 918 0.0504
Sunflower 918 0.0414

Identify which type of oil the student used.

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2b2 marks

The values in the table are for oil at 26°C.

Explain the effect of carrying out the investigation with oil at a lower temperature.

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