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 8.9×10 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?

  • A2.7×10 Pa⋅s
  • B5.3×10 Pa⋅s
  • C17×10 Pa⋅s
  • D32×10 Pa⋅s
  • E11×10 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?

  • A𝐹=6𝜋𝑟𝑣𝜂
  • B𝐹=𝑟𝑣6𝜋𝜂
  • C𝐹=𝜂𝑟𝑣6𝜋
  • D𝐹=6𝜋𝜂𝑟𝑣
  • E𝐹=6𝜂𝑟𝑣𝜋

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?

  • A𝑤=𝐹𝐹
  • B𝑤+𝐹>𝐹
  • C𝑤>𝐹+𝐹
  • D𝑤=𝐹𝐹
  • E𝑤=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/cms, as shown in the diagram. The density of the liquid is 975 kg/m3. Find the dynamic viscosity of the liquid.

Q6:

A sphere of radius 7.5 cm and density 1,500 kg/m3 moves horizontally through water of dynamic viscosity 8.9×10 Pa⋅s. The sphere is decelerating at 4.5×10 m/s2. What is the magnitude of the velocity of the sphere?

Q7:

A solid sphere of radius 1.1 cm and density 1,095 kg/m3 moves vertically downward through a liquid of dynamic viscosity 8.9×10 Pa⋅s and density 1,025 kg/m3, as shown in the diagram. Find the velocity 𝑣 of the sphere.

Q8:

A solid sphere of radius 6.200 mm moves vertically downward at a constant velocity 𝑣=5.500 cm/s through a liquid of dynamic viscosity 8.900×10 Pa⋅s and density 1,025 kg/m3, as shown in the diagram. Find the density of the sphere.

Q9:

A positively charged solid sphere is placed within a fluid. The fluid is within a cylindrical container that has oppositely charged circular faces, as shown in the diagram. The sphere moves vertically upward with a constant velocity 𝑣=12.5 cm/s. The sphere has a radius of 2.2 cm and a density of 1,500 kg/m3. The fluid has a density of 1,450 kg/m3 and a dynamic viscosity of 1.4×10 Pa⋅s. What is the ratio of the magnitude of the electric force acting on the sphere to the magnitude of the drag force acting on the sphere?

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