An 85.0-N backpack is hung from the middle of an aluminum wire, The degree of hung of the wire is 3 degree. The temperature of the wire then drops by 20.0 C¡ã. Find the tension in the wire at the lower temperature. Assume that the distance between the supports does not change.

To find the tension in the wire at the lower temperature, we can use the concept of thermal expansion and the properties of the material (aluminum) to calculate the change in length of the wire.

Here are the steps to find the tension in the wire at the lower temperature:

1. Determine the original length of the wire: For the sake of this explanation, let's assume the original length of the wire is "L" (which remains constant).

2. Calculate the change in temperature: The temperature drops by 20.0 °C, so the change in temperature (∆T) is -20.0 °C.

3. Find the coefficient of linear expansion (α) for aluminum: The coefficient of linear expansion for aluminum is approximately 23 × 10^-6 °C^-1.

4. Use the formula for linear thermal expansion: The change in length (∆L) of a material due to temperature change is given by the formula: ∆L = α * L * ∆T.

Plugging in the values:
∆L = (23 × 10^-6 °C^-1) * L * (-20.0 °C)

5. Calculate the change in length (∆L): Simply multiply the values together to determine the change in length.

6. Determine the new length of the wire: The new length of the wire after the temperature drop is L + ∆L.

7. Calculate the new tension in the wire: Since the backpack is still hung from the middle, the tension in the wire at the lower temperature is divided equally on both sides. Therefore, the tension in each side of the wire is half of the original tension.

T_new = (85.0 N) / 2

Now that you have the new tension in the wire at the lower temperature, you can use the above steps to solve for the actual values of the length and the tension.