A shaft made of aluminum is 40.0 mm in diameter at room temperature (21°C). Its coefficient of thermal expansion = 24.8 x 10-6 mm/mm per °C. If it must be reduced in size by 0.20 mm in order to be expansion fitted into a hole, determine the temperature to which the shaft must be cooled.

Asolid cylinder is concentric with a straight pipe. the cylinder is 0.5 m long and has an outside diameter of 8 cm. the pipe has an inside diameter of 8.5 cm. the annulus between the cylinder ad the pipe contains stationary oil. the oil has a specific gravity of 0.92 and a kinematic viscosity of 5.57 x 10-4 m2/s. most nearly, what is the force needed to move the cylinder along the pipe at a constant velocity of 1 m/s?