An 85.0-N backpack is hung from the middle of an aluminum wire, as the drawing shows. 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.

physics question.

Please fill in the blank to complete the sentence:

Sin of a right angle means the Answer side over the hypotenuse.

To determine the tension in the wire at the lower temperature, we need to account for the change in length of the wire due to the change in temperature, as well as the weight of the backpack.

Here's how you can calculate the tension in the wire at the lower temperature:

1. Determine the original length of the wire: Let's assume the distance between the supports is L.

2. Calculate the change in length of the wire: The change in length of a material due to a change in temperature is given by the equation ΔL = αLΔT, where ΔL is the change in length, α is the coefficient of linear expansion of the material, L is the original length of the material, and ΔT is the change in temperature. The coefficient of linear expansion for aluminum is approximately 0.000022/°C.

ΔL = (0.000022/°C)(L)(-20.0°C)

3. Calculate the new length of the wire: The new length of the wire is given by L' = L + ΔL.

4. Calculate the tension in the wire: The tension in the wire can be determined by balancing the vertical forces acting on the wire.

Tension in wire = Weight of backpack + Weight of wire

Weight of backpack = m * g, where m is the mass of the backpack and g is the acceleration due to gravity (approximately 9.8 m/s^2).

Weight of wire = m_wire * g, where m_wire is the linear mass density of the wire (mass per unit length) and g is the acceleration due to gravity.

The linear mass density of the wire can be calculated as m_wire = ρ * A, where ρ is the density of the wire and A is the cross-sectional area of the wire.

5. Substitute the calculated values into the equation to find the tension in the wire.

It's important to note that the density of the wire and its cross-sectional area, as well as the distance between the supports, are not provided in the question. You would need this additional information to calculate the tension accurately.