"This session we began by checking the student's homework and correcting mistakes that he did. I found that he has a tendency to find an equation and then plug it into his calculator in order to find the answer. I told him that not always will he be given numerical values, and that he should try his best to do the math by hand: manipulating the variables around in order to obtain an answer before any numbers are plugged in. We corrected the rest of the problems and moved on.
This session we talked about momentum and fluid dynamics. We began momentum by listing the formula for momentum: mass times velocity. We also said that momentum is equal to force times a time interval that the force acts on an object.
We began with the baseball bat problem, in which you have to use both relations for momentum. You are given the time that the ball is in contact with the bat, the initial and final velocity of the ball, and the mass of the ball. You need to realize that the change in velocity is the magnitude of the initial velocity plus the magnitude of the final velocity. This is because the bat had to slow the ball down and then speed it back up. Then you plug and chug.
We moved on to the inelastic collision problem. We reviewed that for any collision problem, you will need to ask yourself about the total momentum in the x direction (initial and final) and write an equation for it, and the total momentum in the y direction (initial and final) and write an equation for that. You then find the final portion of the x and y velocity and then use vector addition to find the total final velocity of the two objects now stuck together and the angle that they move away with.
We then went onto the elastic collision problem. We reviewed that momentum is still conserved, and so you end up using the same method, but that the objects do not stick together anymore, and so you need to figure out the final velocity of each projectile.
We then moved on to fluid dynamics. We reviewed the three main parts: Archimedes principle, which states that the buoyant force on the object is equal to the weight of the water that the object displaces. We reviewed how to write the mass of the displaced water in terms of the density of water and the portion of the volume of the submerged object.
We reviewed Pascal's principle, which says that a fluid that is pressurized is exerted out in every direction from the fluid to its surroundings. We then had a larger conversation about pressure, and wrote down the equation for pressure and reviewed how to re-write the weight of the water, and then for a column of fluid how to rewrite the volume of the fluid. Combining these yields a relation for the pressure exerted by a fluid overhead.
We then went on to review Bernoulli's equation, which is essentially the conservation of energy when applied to fluids. I showed the student why the equation makes sense, and that it is essentially our conversation of energy equation multiplied by the volume of the fluid.
This brought us right up to the end of the session. The student learned an amazing amount of Physics in a very brief amount of time. Excellently done: five out of five stars overall."