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

23 mins4 questions
1a
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2 marks

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.

1b
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2 marks

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

1c
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3 marks

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

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1a
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3 marks

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.

1b
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6 marks

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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4 marks

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.

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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