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An electric drill with a steel drill bit of mass m = 27.0 g and diameter 0.635 cm is used to drill into a cubical steel block of mass M = 240 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 m's and exerts a force of constant magnitude 3.20 N on the block. As shown in Figure, 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 tumed on and drills into the block fora time interval of 15.0 s. Lets 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 euts three- quarters of the way through the block during 15.0 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-cighth of the way through the block in 15.0 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.

An electric drill with a steel drill bit of mass m = 27.0 g and diameter 0.635 cm is used to drill into a cubical steel block of mass M = 240 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 m's and exerts a force of constant magnitude 3.20 N on the block. As shown in Figure, 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 tumed on and drills into the block fora time interval of 15.0 s. Lets 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 euts three- quarters of the way through the block during 15.0 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-cighth of the way through the block in 15.0 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.

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An electric drill with a steel drill bit of mass m = 27.0 g and diameter 0.635 cm is used to drill into a cubical steel block of mass M = 240 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 m/s and exerts a force of constant magnitude 3.20 N on the block. As shown in Figure, 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 tumed on and drills into the block fora time interval of 15.0 s. Lets 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 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 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.
Transcribed Image Text:An electric drill with a steel drill bit of mass m = 27.0 g and diameter 0.635 cm is used to drill into a cubical steel block of mass M = 240 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 m/s and exerts a force of constant magnitude 3.20 N on the block. As shown in Figure, 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 tumed on and drills into the block fora time interval of 15.0 s. Lets 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 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 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.
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