Two horizontal wires are joined end to end, each with a diameter of 2.000 mm. The two joined wires are connected to fixed points a total distance of 4.00000 m apart. When both wires are at a temperature of 36.0°C, each wire has an unstretched length of 2.00000 m, and the tension in each is negligible. The first wire is made of steel and extends from x = -2.00000 m to x = 0, and the second is made of aluminum and extends from x = 0 to x = 2.00000 m. The temperature of both wires is then lowered to 11.0°C, and the wires stay joined together as they cool. The steel wire is composed of an alloy that has an average coefficient of linear expansion of 1.10 × 10-5(°C)-¹ and a Young's modulus of 2.00 x 10¹¹ N/m². The aluminum wire is composed of an alloy that has an average coefficient of linear expansion of 2.40 x 10-5(°C)-1 and a Young's modulus of 7.00 x 10¹0 N/m². (Due to the nature of this problem, do not use rounded intermediate values in your calculations-including answers submitted in WebAssign.) (a) At the final, lower temperature, what is the x-coordinate (in m) of the junction between the wires? m (b) At the final, lower temperature, what is the tension (in N) in the wire? N
Two horizontal wires are joined end to end, each with a diameter of 2.000 mm. The two joined wires are connected to fixed points a total distance of 4.00000 m apart. When both wires are at a temperature of 36.0°C, each wire has an unstretched length of 2.00000 m, and the tension in each is negligible. The first wire is made of steel and extends from x = -2.00000 m to x = 0, and the second is made of aluminum and extends from x = 0 to x = 2.00000 m. The temperature of both wires is then lowered to 11.0°C, and the wires stay joined together as they cool. The steel wire is composed of an alloy that has an average coefficient of linear expansion of 1.10 × 10-5(°C)-¹ and a Young's modulus of 2.00 x 10¹¹ N/m². The aluminum wire is composed of an alloy that has an average coefficient of linear expansion of 2.40 x 10-5(°C)-1 and a Young's modulus of 7.00 x 10¹0 N/m². (Due to the nature of this problem, do not use rounded intermediate values in your calculations-including answers submitted in WebAssign.) (a) At the final, lower temperature, what is the x-coordinate (in m) of the junction between the wires? m (b) At the final, lower temperature, what is the tension (in N) in the wire? N
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Transcribed Image Text:Two horizontal wires are joined end to end, each with a diameter of 2.000 mm. The two joined wires are connected to fixed points a total distance of 4.00000 m
apart. When both wires are at a temperature of 36.0°C, each wire has an unstretched length of 2.00000 m, and the tension in each is negligible. The first wire is
made of steel and extends from x = -2.00000 m to x = 0, and the second is made of aluminum and extends from x = 0 to x = 2.00000 m. The temperature of
both wires is then lowered to 11.0°C, and the wires stay joined together as they cool.
The steel wire is composed of an alloy that has an average coefficient of linear expansion of 1.10 x 10-5 (°C)-¹ and a Young's modulus of 2.00 x 10¹¹ N/m². The
aluminum wire is composed of an alloy that has an average coefficient of linear expansion of 2.40 x 10-5(°C)-¹ and a Young's modulus of 7.00 x 10¹0 N/m².
(Due to the nature of this problem, do not use rounded intermediate values in your calculations-including answers submitted in WebAssign.)
(a) At the final, lower temperature, what is the x-coordinate (in m) of the junction between the wires?
m
(b) At the final, lower temperature, what is the tension (in N) in the wire?
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