Viscous drag and Stokes' lawEdexcel A-Level Physics: Subtopic test

1. 1
   A steel ball bearing of radius 1.5 mm moves slowly through glycerol of viscosity 1.4 Pa s. The flow around the ball is laminar.

   (a)

   Which of these is the correct unit for viscosity, as derived from F = 6πηrv?

   [1 mark]

   • AN m⁻² s⁻¹
   • BN m s⁻¹
   • CN s m⁻²
   • Dkg m s⁻²

   (b)

   The ball moves at 0.020 m s⁻¹. What is the viscous drag force on it?

   [1 mark]

   • A7.9 × 10⁻⁴ N
   • B2.5 × 10⁻⁴ N
   • C1.6 × 10⁻³ N
   • D7.9 × 10⁻⁷ N

   (c)

   The ball is released from rest in a deep tank of glycerol. Explain why it eventually falls at a constant speed.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   A student drops identical steel balls through a tall column of oil and measures the terminal velocity. At 20 °C the terminal velocity is 0.048 m s⁻¹ and at 50 °C it is 0.31 m s⁻¹. Assume that the density of the oil is the same at both temperatures and that Stokes' law applies.

   (a)

   Which statement describes how the viscosity of the oil changes as its temperature rises?

   [1 mark]

   • AIt increases, because faster molecules collide more often with the ball
   • BIt stays the same, because viscosity depends only on the density of the oil
   • CIt increases in proportion to the temperature
   • DIt decreases

   (b)

   By what factor is the viscosity of the oil at 20 °C greater than at 50 °C?

   [1 mark]

   • A0.15
   • B6.5
   • C0.26
   • D42

   (c)

   Explain why the balls reach a higher terminal velocity in the oil at 50 °C.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A steel ball of radius 2.0 mm and density 7800 kg m⁻³ falls at its terminal velocity of 0.085 m s⁻¹ through an oil of density 920 kg m⁻³. The flow is laminar. Take g = 9.81 N kg⁻¹. The volume of a sphere is 4πr³/3.

   (a)

   Calculate the weight of the ball minus the upthrust on the ball.

   [3 marks]

   (b)

   Determine the viscosity of the oil.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   In a core practical, a student determines the viscosity of glycerol by timing steel balls as they fall through glycerol in a tall transparent measuring cylinder at room temperature. The student has a micrometer, a balance, a metre rule, a stopwatch and some elastic bands to use as markers. The densities of steel and of glycerol are known.

   (a)

   Describe how the student should carry out the experiment to determine the viscosity of glycerol.

   [6 marks]

   (b)

   The student uses steel balls of radius 2.0 mm and density 7800 kg m⁻³ in a cylinder of internal diameter 2.0 cm containing glycerol of density 1260 kg m⁻³ at about 20 °C. She starts the stopwatch as she releases each ball at the surface and stops it as the ball passes a mark 20 cm below, finding an average speed of 0.030 m s⁻¹. Using η = F/(6πrv), with F equal to the weight minus the upthrust, she calculates a viscosity of 1.9 Pa s. The data book value for glycerol at 20 °C is 1.4 Pa s. Evaluate possible reasons for the difference between her value and the data book value.

   [6 marks]

   Total for question 4: 12 marks

End of questions