A one-piece cylinder has a core section protruding from the larger drum and is free to rotate around its central axis. A rope wrapped around the drum of radius 1.39 m exerts a force of 3.34 N to the right on the cylinder. A rope wrapped around the core of radius 0.48 m exerts a force of 8.52 N downward on the cylinder. What is the magnitude of the net torque acting on the cylinder about the rotation axis? Answer in units of N ∗ m.

How many milliliters of water at 23 °c with a density of 1.00 g/ml must be mixed with 180 ml (about 6 oz) of coffee at 95 °c so that the resulting combination will have a temperature of 60 °c? assume that coffee and water have the same density and the same specific heat. how much will the temperature of a cup (180 g) of coffee at 95 °c be reduced when a 45 g silver spoon (specific heat 0.24 j/g °c) at 25 °c is placed in the coffee and the two are allowed to reach the same temperature? assume that the coffee has the same density and specific heat as water. a 45-g aluminum spoon (specific heat 0.88 j/g °c) at 24 °c is placed in 180 ml (180 g) of coffee at 85 °c and the temperature of the two become equal. (a) what is the final temperature when the two become equal? assume that coffee has the same specific heat as water. (b) the first time a student solved this problem she got an answer of 88 °c. explain why this is clearly an incorrect answer.