A soccer player kicks a ball, changing its momentum by 11\, \dfrac {\text{kg}\cdot \text m}{\text s}11 s kg⋅m 11, start fraction, start text, k, g, end text, dot, start text, m, end text, divided by, start text, s, end text, end fraction. The net force on the ball is 910\,\text N910N910, start text, N, end text.

Athin electrical heater is inserted between a long circular rod and a concentric tube with inner and outer radii of 20 and 40 mm. the rod (a) has a thermal conductivity of ka = 0.15 w/(m*k), while the tube (b) has a thermal conductivity of kb = 0.8 w/(m*k) and its outer surface is subjected to convection with a fluid of temperature t= -15°c and heat transfer coefficient 60 w/(m2 *k). the thermal contact resistance between the cylinder surfaces and the heater is negligible. (a) determine the electrical power per unit length of the cylinders (w/m) that is required to maintain the outer surface of cylinder b at 15°c. (b) what is the temperature at the center of cylinder a?