Question

a sonometer wire having cross section area 0.85×10^-6 is stretched between two rigid supports 1.2 m apart. A tension of 20 N is applied at its free end. If the temperature is reduced by 12℃, calculate the final tension in the wire. Take coefficient of linear expansion and isothermal Young's modulus to be 1.5×10^-5K^-1 and 2.0×x10^11 Nm^-2, respectively.

Answer 1

Answer on Question #67076-Physics-Molecular Physics-Thermodynamics

A sonometer wire having cross section area $0.85 \times 10^{\wedge} - 6$ is stretched between two rigid supports $1.2\mathrm{m}$ apart. A tension of $20\mathrm{N}$ is applied at its free end. If the temperature is reduced by $12{}^{\circ}\mathrm{C}$ , calculate the final tension in the wire. Take coefficient of linear expansion and isothermal Young's modulus to be $1.5 \times 10^{\wedge} - 5\mathrm{K}^{\wedge} - 1$ and $2.0 \times 10^{\wedge}11\mathrm{Nm}^{\wedge} - 2$ , respectively.

Solution

$$\Delta F = - A \gamma \alpha \Delta T$$ $$\Delta F = (0. 8 5 \cdot 1 0 ^ {- 6}) (2 \cdot 1 0 ^ {1 1}) (1. 5 \cdot 1 0 ^ {- 5}) (1 2) =$$ $$F ^ {\prime} = F + \Delta F = 2 0 + 3 0. 6 = 5 0. 6 N.$$

Answer: 50.6 N.

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