In ancient times there was one great kingdom on whose throne was a just but cruel king named Physicus. King Physicus had his subjects. There were a total of ten subjects. At the end of each year, each of them brought the king ten bars of gold. Each gold bar weighed one kilogram. So, each subject had to hand over ten kilograms of gold to the king. The king's spy informed King Physicus that one subject was making a hundred grams lighter bar, but that they looked the same in size, the only difference was in the density of the gold. King Physicus was a wise man and with one measurement on the scales he found out which subject was stealing from him. The question is: how did King Physicus find out who the thief was with just one measurement?

Aplane takes off from an airport and flies to town a, located d1 = 215 km from the airport in the direction 20.0° north of east. the plane then flies to town b, located d2 = 230 km at 30.0° west of north from town a. use graphical methods to determine the distance and direction from town b to the airport. (enter the distance in km and the direction in degrees south of west.)

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).

When you turn on a battery-operated device, an electrical circuit is