I have access to a remote controlled submersible and I want to use it to do some physics with some students of mine. We are examining Newton's Laws. I intend to use spring scales to determine the mass of the sub and the max force the sub can exert by applying full forward thrust while reading a spring scale attached to the sub. We'll then have the sub push floating containers of various weights across a tank to record the times. We'll use Δx = ½ a (Δt)^2 and F=ma to calculate the acceleration for each trial and then compare the results. My issue is that this is good as far as it goes, but... 1. Δx = ½ a (Δt)^2 will yield bad data because acceleration won't be constant. 2. F=ma will yield bad data because we can't calculate the force of friction (drag) to determine the net force. I think it will be worth doing to get practice collecting data and making calculations as long as we discuss the previous two points, but I'm looking for some help in making the calculations a little more realistic. Any ideas?
This is more complicated than you apparently think. For example The thrust of the sub will depend on its velocity relative to the water, and the relationship between thrust and speed will depend on what type of propulsion system it has (e.g. propellor or water jet). The effective mass of the system is not equal to its physical mass, because the objects can't move unless some water moves in the opposite direction. This is hard to quantify because it depends not only on the shape of the objects, but also on the width and depth of the water channel. It's an important reason why fluid flow experimenters prefer to have steady flow conditions, not accelerating ones. If this is part of an "intro to physics" or "intro to mechanics" course, maybe you would be better with a simpler situation, despite the "cool factor" of the submarine, unless you are sure your students can handle so many deviations from the basic notion of "F = ma" without getting lost, and they have the enough math skills to quantify them (which probably means calculus).
IDK why you want to use a submersible to experiment with and demonstrate Newton's Laws of motion, unless you just want to play with boats in a bathub. There are simpler experimental setups (land-based, unfortunately) which can be used that don't include all of the uncertainties you mentioned in the OP. Save the boats for when your students have grasped the basics.
I agree. I'm trying to do physics with a focus on maritime applications. Thus the difficulty. Another idea would be to use wheeled carts with sails and a fan to investigate how sails work and focus on some net force and acceleration calculations.
Fair enough, but I think the danger is that the students (especially the less smart ones) take away the message that "F = ma" doesn't actually apply to real life, it's just something you have to learn to pass the course.
Again, I agree. I think I'll most likely leave the submersible till we hit buoyancy and displacement, and instead focus on carts on an air-track fitted out with sails to investigate net force and aerodynamics, etc... Just as a follow-up though, how does one go about examining friction and other forces on a submerged object in real life anyway? Is there any applicable way to do it with a limited calculus background?
Well, 100 years ago literally nobody had figured out how to do it for general real-world flow situations, until Prandtl invented boundary layer theory. Until the 1980s the required amount of computing power was too expensive for general use - but a cheap PC today is much more powerful that the Cray supercomputers of the 1980s. You won't be able to do much "pen and paper" work with only "calculus lite". I would say the practical way today is get a CFD software package and learn how to use it. I'm not a fluids specialist and what experience I have is with gases not liquids, so I don't know what is most appropriate for your applications. It might be worth searching for some higher level courses (e.g. http://www.southampton.ac.uk/engine...ce_maritime_computational_fluid_dynamics.page) and contacting their academic staff for advice.
It's not clear what equipment you have access to, but if you want to investigate friction due to fluid drag, a dynamometer would be a useful tool to have. Towing models in a test tank is still a useful procedure when investigating resistance and propulsion problems for marine vehicles.