George washington gale ferris, jr., a civil engineering graduate from rensselaer polytechnic institute, built the original ferris wheel for the 1893 world's columbian exposition in chicago. the wheel, an astounding engineering construction at the time, carried 36 wooden cars, each holding up to 60 passengers, around a circle 76 m in diameter. the cars were loaded 6 at a time, and once all 36 cars were full, the wheel made a complete rotation at constant angular speed in about 2 min. estimate the amount of work that was required of the machinery to rotate the passengers alone. assume each passenger had a mass of 89 kg.

An electron and a proton have the same kinetic energy upon entering a region of constant magnetic field and their velocity vectors are perpendicular to the magnetic field. suppose the magnetic field is strong enough to allow the particles to circle in the field. note: you'll need to look up the masses for an electron and proton. 1) what is the ratio of the radii of their circular paths rp/re?

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).

Imagine that someone pushes one marble toward a motionless marble. would there still be action-reaction forces involved in the collision? how might the marbles’ motions be changed? ?