One end of a string is attached to a rigid wall on a tabletop. The string is run over a frictionless pulley and the other end of the string is attached to a stationary hanging mass. The distance between the wall and the pulley is 0.405 meters, When the mass on the hook is 25.4 kg, the horizontal portion of the string oscillates with a fundamental frequency of 261.6 Hz (the same frequency as the middle C note on a piano). Calculate the linear mass density of the string.

Steam is generated in a boiler of a cogeneration plant at 10 mpa and 450°c at a steady rate of 5 kg/s. in normal operation, steam expands in a turbine to a pressure of 0.5 mpa and is then routed to the process heater, where it supplies the process heat. steam leaves the process heater as a saturated liquid and is pumped to the boiler pressure. in this mode, no steam passes through a condenser, which operates at 20 kpa. (a) determine the power produced in the turbine and the rate at which process heat is supplied in this mode. (b) determine the power produced in the turbine and the rate of process heat supplied if only 60 percent of the steam is routed to the process heater and the remainder is expanded to the condenser pressure. (3.32 mw; 9.69 mw; 4.25 mw; 5.82 mw)

The temperature at a point (x, y) is t(x, y), measured in degrees celsius. a bug crawls so that its position after t seconds is given by x = 6 + t , y = 8 + 1 3 t, where x and y are measured in centimeters. the temperature function satisfies tx(3, 9) = 5 and ty(3, 9) = 4. how fast is the temperature rising on the bug's path after 3 seconds? (round your answer to two decimal places.)

Which of the following best describes internal energy? a. the difference between the kinetic and potential energies of the particles in a system b. the sum of the kinetic and potential energies of the particles in a system c. the sum of the kinetic and thermal energies of the particles in a system d. the difference between the kinetic and thermal energies of the particles in a system