Two substances, a and b, initially at different temperatures, come into contact and reach thermal equilibrium. the mass of substance a is 6.42 g and its initial temperature is 20.7 oc. the mass of substance b is 26 g and its initial temperature is 52.5 oc. the final temperature of both substances at thermal equilibrium is 46.1 oc. if the specific heat capacity of substance b is 1.17 j/gâoc, what is the specific heat capacity of substance a?

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.