Worksheet: Stokes' Law

In this worksheet, we will practice calculating the friction force acting on a sphere as it travels through a viscous fluid.

Q1:

What is the magnitude of the force due to fluid friction exerted on a sphere of radius 15 cm that moves horizontally at 15 cm/s through water of dynamic viscosity 8 . 9 × 1 0 Pa⋅s?

Q2:

A sphere of radius 12 cm moves horizontally at 20 cm/s through a liquid that produces a fluid friction force of magnitude 240 μN. What is the dynamic viscosity of the liquid?

  • A 1 1 × 1 0 Pa⋅s
  • B 3 2 × 1 0 Pa⋅s
  • C 2 . 7 × 1 0 Pa⋅s
  • D 5 . 3 × 1 0 Pa⋅s
  • E 1 7 × 1 0 Pa⋅s

Q3:

Which of the following formulas correctly relates 𝐹 , the fluid friction force; 𝜂 , the dynamic viscosity; 𝑟 , the radius of a sphere; and 𝑣 , the velocity with which the sphere moves through the fluid?

  • A 𝐹 = 6 𝜋 𝜂 𝑟 𝑣
  • B 𝐹 = 6 𝜂 𝑟 𝑣 𝜋
  • C 𝐹 = 6 𝜋 𝑟 𝑣 𝜂
  • D 𝐹 = 𝜂 𝑟 𝑣 6 𝜋
  • E 𝐹 = 𝑟 𝑣 6 𝜋 𝜂

Q4:

A solid sphere moves vertically downward through water at a constant velocity 𝑣 , as shown in the diagram. The forces acting on the sphere are its weight, 𝑤 , the upthrust from the water, 𝐹 , and the fluid friction due to the water, 𝐹 . Which of the following equations correctly shows the relation of these forces to each other?

  • A 𝑤 + 𝐹 > 𝐹
  • B 𝑤 > 𝐹 + 𝐹
  • C 𝑤 = 𝐹 𝐹
  • D 𝑤 = 𝐹 𝐹
  • E 𝑤 = 𝐹 + 𝐹

Q5:

A solid sphere of radius 1.5 cm and density 1,050 kg/m3 moves vertically downward through a liquid at a constant velocity 𝑣 = 1 . 2 / c m s , as shown in the diagram. The density of the liquid is 975 kg/m3. Find the dynamic viscosity of the liquid.

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