The aurora is caused when electrons and protons, moving in the earth's magnetic field of ≈5.0×10−5t, collide with molecules of the atmosphere and cause them to glow. part a what is the radius of the circular orbit for an electron with speed 4.0×106 m/s ? assume that the electron moves in a plane perpendicular to the magnetic field. express your answer with the appropriate units.

Part f - example: finding two forces (part i) two dimensional dynamics often involves solving for two unknown quantities in two separate equations describing the total force. the block in (figure 1) has a mass m=10kg and is being pulled by a force f on a table with coefficient of static friction îľs=0.3. four forces act on it: the applied force f (directed î¸=30â above the horizontal). the force of gravity fg=mg (directly down, where g=9.8m/s2). the normal force n (directly up). the force of static friction fs (directly left, opposing any potential motion). if we want to find the size of the force necessary to just barely overcome static friction (in which case fs=îľsn), we use the condition that the sum of the forces in both directions must be 0. using some basic trigonometry, we can write this condition out for the forces in both the horizontal and vertical directions, respectively, as: fcosî¸â’îľsn=0 fsinî¸+nâ’mg=0 in order to find the magnitude of force f, we have to solve a system of two equations with both f and the normal force n unknown. use the methods we have learned to find an expression for f in terms of m, g, î¸, and îľs (no n).

Avehicle has an oil leak that is causing the entire oil pan to be wet, but inspection reveals no exact source after cleaning off the oil residue. technician a says to install a fluorescent dye in the crankcase and operate the engine, then re-inspect for leaks with a special light (black light). technician b says the oil leak may be coming from a source at the top of the engine, such as a valve cover gasket. who is correct?

What is the force that opposes motion and works against the downward pull? a) friction b) gravity c) weight d) acceleration