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“If we worked on the assumption that what is accepted as true really is true, then there would be little hope for advance” - Orville Wright“No flying machine will ever fly from New York to Paris ... [because] no known motor can run at the requisite speed for four days without stopping.”- Orville Wright
Skills - Gravitation Correctly apply universal law of gravitation: Spherical symmetry / small objects, c.m. (<< r) / No force inside spherical shell Find satellite speeds for circular orbits Use conserv of L to find satellite speed in elliptical orbit, given speed elsewhere in same orbit. (Kepler #2) Understand difference between weight and apparent weight (astronauts in orbit are falling!) Understand implications of elliptical orbits (e.g., you can’t throw a rock into orbit! Why not?) Find escape speed from a spherical planet.
Skills - Periodic Motion •Memorize relationships between T, f, •Predict changes in motion when mass is added to or removed from a mass-spring system, at different points in its oscillation •Given sufficient information (spring constant, mass, initial conditions) predict where a mass will be at a later time. (This means writing down the equation of motion correctly!) •(Find k! Either from a known force and displacement, F- -kx, or from the frequency and mass in SHM) •Given equation sqrt(k/m), solve angular SHM problems by analogy! •Apply simple pendulum equation (to be given). •Apply physical pendulum equation (to be given). YOU MUST memorize what d and I mean in this equation.
Skills - Fluids • Understand density and pressure. Pressure is same at same depth in same (stationary) fluid. Use to calculate mechanical advantage in a hydraulic lift. • Understand difference between gauge pressure and total pressure. • Apply P=gh (given) correctly. When can it NOT be used? • Solve buoyancy problems, even if two fluids are involved (Use FBDs when needed!) • Apply Bernoulli to solve for flow velocity, or for pressure, or height, for incompressible flows. (BE will be given).
• Given wavelength and frequency, write down the mathematical description of a wave moving in either the + or - direction. Apply (given) equation for speed of waves on a string. • Memorize and appy relationship between frequency, wavelength, and wave speed. • Understand difference between transverse and longitudinal waves. • Memorize that power & intensity are proportional to amplitude squared. Apply inverse square law for waves in 3D. • Use principle of superposition to sketch interfering waves (on a string). • Understand what a standing wave is, and predict frequencies for overtones on a violin string. Skills - Waves
An incompressible fluid flows through a constriction, as shown. The speed of the fluid isA] faster at (a) than at (b)B] faster at (b) than at (a)C] the same speed at both places
The fluid moves faster at (b) becauseA] being incompressible, the smaller cross-sectional area forces the velocity to be higherB] there is a pressure drop from (a) to (b) that accelerates the fluidC] either is a legitimate viewpoint, but I prefer B, as it helps me to understand Bernoulli.
There is a subtlety here: we do NOT apply Bernoulli to points A and B directly, because they are not “connected” by smooth (laminar) flow lines. In which tube would the fluid rise higher? Or choose [C], the fluid would rise to the same height in both tubes? The pressure at b is lower, so the fluid will not rise as high in tube b. Note: Pascal’s principle (equal pressures at equal heights) applies to static fluid only!
