An electric drill with a steel drill bit of mass 27.0 g anddiameter of 0.635 cm

Question

An electric drill with a steel drill bit of mass 27.0 g anddiameter of 0.635 cm is used to drill into a cubical steel block ofmass 240 g. Assume steel has the same properties as iron. Thecutting process can be modeled as happening at one point onthe circumference of the bit. This point moves in a spiral atconstant speed 40.0 m/s and exerts a force of constant magnitude3.20 N on the block. As shown in Figure P20.8, a groove in the bitcarries the chips up to the top of the block, where they from apile around the hole. The block is held in a clamp made of materialof low thermal conductivity, and the drill bit is held in a chuckalso made of this material. We consider turning the drill on for atime interval of 15.0 s. This time interval is sufficiently shortthat the steel objects lose only a negligible amount of energy byconduction, convention, and radiation into their environment.Nevertheless, 15 s is long enough for conduction within the steelto bring it all to a uniform temperature. The temperature ispromptly measured with a thermometer probe, shown in the side ofthe block in the figure. (a) Suppose the drill bit is sharp andcuts three-quarters of the way through the block during 15 s. Findthe temperature change of the whole quantity of steel. (b)What if? Now suppose the drill bit is dull andcuts only one-eighth of the way through the block. Identify thetemperature change of the whole quantity of steel in this case. (c)What pieces of data, if any, are unnecessary for the solution?Explain.

Explanation / Answer

a) T = 900 K b) T =1050 K c) Force is unnecessary

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