the 2010 nobel prize in physics was awarded for the discovery of graphene, a two-dimensional form of carbon in which the atoms form a two-dimensional crystal-lattice sheet only one atom thick.

A500g object falls off a cliff and losers 100 j from its gravitational potential energy store. if the gravitational field strength g=9.8n/kg, how high is the cliff?

The average density of the planet uranus is 1.27 103 kg/m3. the ratio of the mass of neptune to that of uranus is 1.19. the ratio of the radius of neptune to that of uranus is 0.969. find the average density of neptune.

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.