Introducing the new series of ‘Question of the Week’ (QotW) where I pose physics and math questions to myself and others. These QotW are meant to explore concepts and generally have a little fun. I am no expert in these so it may very well be that my solutions are wrong and I invite criticism and scrutiny.
When I clean dishes (I do!) and encounter a dirty jam jar, milk bottle or similar container I occasionally consider how much water to put in the container before shaking it. The idea being that the more water (mass) I have inside the more force the water will hit the dirty corners with. The catch is that the more water I put in the jar the less distance it will have to accelerate when I shake the jar and hit the other end. So the question is how much of the container should be filled with water to maximize the force with which the water hits the other side of the jar.