Suppose that a marble is sinking in honey. The marble is subject to frictional force opposing...

Transcribed Image Text:

Suppose that a marble is sinking in honey. The marble is subject to frictional force opposing its fall. The frictional force is proportional to the velocity of the marble. Suppose that there is also a resistive buoyant force exerted by the honey. According to Archimedes principle, the buoyant force is equal to the weight of the honey displaced by the marble. Let m be the mass of the marble and let H be the mass of the honey displaced by the marble. (1 mark) Draw a diagram showing the forces acting on the marble as it sinks in the honey. (2 marks) Let u(t) be the velocity of the marble at time t. Write a differential equation modelling the velocity of the marble. (1 mark) Determine the equilibrium solution, v=vo, of the differential equation. ď²v (2 marks) Show that for u<vo, < 0. dt2 (2 marks) Sketch (by hand) a solution curve.. Suppose that a marble is sinking in honey. The marble is subject to frictional force opposing its fall. The frictional force is proportional to the velocity of the marble. Suppose that there is also a resistive buoyant force exerted by the honey. According to Archimedes principle, the buoyant force is equal to the weight of the honey displaced by the marble. Let m be the mass of the marble and let H be the mass of the honey displaced by the marble. (1 mark) Draw a diagram showing the forces acting on the marble as it sinks in the honey. (2 marks) Let u(t) be the velocity of the marble at time t. Write a differential equation modelling the velocity of the marble. (1 mark) Determine the equilibrium solution, v=vo, of the differential equation. ď²v (2 marks) Show that for u<vo, < 0. dt2 (2 marks) Sketch (by hand) a solution curve..

Answer rating: 100% (QA)

Solution Step1 Diagram showing the forces acting on the marble as it sinks in the honey positive dir... View the full answer