You and your team are given the task of constructing a crude thermometer that covers a temperature range from 0 °C to 60 °C. You have at your disposal an aluminum rod of length L₀ = 2.00 m (at T = 0 °C) and diameter D = 0.50 cm, and a broken clock that is missing its hour hand, and its longer minute hand is hanging loose and pointing in the six o’clock direction. The long hand of the clock is 8.20 inches long and pivots loosely at the clock’s center. You get the idea to mount the rod horizontally so that one end butts against a wall and the other end pushes against the dangling minute hand of the clock. A temperature-induced change in the length of the rod will then be reflected in a change in the angle that the minute hand makes with the vertical (i.e., relative to the six o’clock position).

(a) If you want the full temperature range to span the angle between the 6 and 7 markings (uniformly spaced) on the clock, how far from the central pivot should the end of the rod make contact with the minute hand?

(b) The current temperature in the room is 65.0 °F. At what angle relative to the vertical (the six o’clock position) should the minute hand point at this temperature if it is to point directly at 6 when T = 0 °C?

(c) What would be the angular range of your “clock-thermometer” if the rod were made of steel, rather than aluminum? Assume that it is placed at the same position on the minute hand as determined in (a).