Serway & Jewett — The First Law of Thermodynamics: Problem 8.

An electric drill with a steel drill bit of mass \( m = 27.0 \text{ g} \) and diameter \( 0.635 \text{ cm} \) is used to drill into a cubical steel block of mass \( M = 240 \text{ g} \). Assume steel has the same properties as iron. The cutting process can be modeled as happening at one point on the circumference of the bit. This point moves in a helix at constant tangential speed \( 40.0 \text{ m/s} \) and exerts a force of constant magnitude \( 3.20 \text{ N} \) on the block. As shown in Figure P19.8 (page 528), a groove in the bit carries the chips up to the top of the block, where they form a pile around the hole. The drill is turned on and drills into the block for a time interval of \( 15.0 \text{ s} \). Let’s assume this time interval is long enough for conduction within the steel to bring it all to a uniform temperature. Furthermore, assume the steel objects lose a negligible amount of energy by conduction, convection, and radiation into their environment. (a) Suppose the drill bit cuts three-quarters of the way through the block during \( 15.0 \text{ s} \). Find the temperature change of the whole quantity of steel. (b) What If? Now suppose the drill bit is dull and cuts only one-eighth of the way through the block in \( 15.0 \text{ s} \). Identify the temperature change of the whole quantity of steel in this case. (c) What pieces of data, if any, are unnecessary for the solution? Explain.