8. two solid cylindrical specimens a and b, made of a perfectly plastic material, are being forged with friction and isothermally at room temperature to a reduction in height of 50%. specimen a has a height of 50 mm and a cross-sectional area of 6.25×10-4m2 and specimen b has a height of 25 mm and a cross-sectional area of 0.0025 m2. will the work done be the same for the two specimens? explain.

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.