A small mass m is tied to a string of length L and is whirled in vertical circular motion. The speed of the mass v is such that the ratio of the string tension at the top of the circle to that at the bottom of the circle is FtopT/FbotT = 0.5. Derive an expression for the speed v.

The law of conservation of energy states that energy cannot be created or , energy can be from one substance to another. the first blank is ' destroyed ' and for the second blank is ' transferred '

Consider a double atwood machine constructed as follows: a mass 4m is suspended from a string that passes over a massless pulley on frictionless bearings. the other end of this string supports a second similar pulley, over which passes a second string supporting a mass of 3m at one end and m at the other. using two suitable generalized coordinates, set up the lagrangian and use the lagrange equations to find the acceleration of the mass 4m when the system is released. explain why the top pulley rotates even though it carries equal weights on each side.

Sodium chloride, nacl, is formed when a sodium atom transfers its electron to a chlorine atom. the difference in charge between the two atoms creates a(n) attraction that bonds them together.