A copper wire of diameter 0.30mm and length 1.50m is joined to another steel wire of same diameter and length 1.20m. The copper part of the double wire is hung vertically to a fixed point, while a small weight is connected to the lower end of the steel part. Joining the two wires tighter has lead to compression of each one of them by 20mm. Later a 30N weight is connected to the lower point of the steel part. Calculate:

a.The stress in each wire
b.The strain of each wire, knowing that Young modulus of copper is 1.3 x 10^11 N/m^2 and of steel is 2.0 x 10^11 N/m^2
c.The total elongation of both wires

To answer these questions, we need to use the formulas for stress, strain, and elongation.

a. Stress in each wire:
Stress is defined as the force applied per unit area. To calculate the stress in each wire, we need to divide the force applied by the cross-sectional area of the wire.

Stress (σ) = Force (F) / Cross-sectional Area (A)

For the copper wire:
Given that the diameter (d) of the wire is 0.30 mm, we can calculate the radius (r) as half the diameter:
r = d / 2 = 0.30 mm / 2 = 0.15 mm = 0.15 × 10^(-3) m

We also know that the length (L) of the copper wire is 1.50 m. The compression of each wire is given as 20 mm, which means the effective length (L_eff) of the copper wire is L - compression.

L_eff = L - compression = 1.50 m - 20 mm = 1.50 m - 0.020 m = 1.48 m

The cross-sectional area (A) of the wire can be calculated using the formula:
A = π * r^2

Substituting the values into the formula, we can find the cross-sectional area of the copper wire.

Stress_copper = F / A_copper

For the steel wire:
The calculations are the same, as the diameter, length, and compression are given for both wires.

Stress_steel = F / A_steel

b. Strain in each wire:
Strain is a measure of the deformation or elongation of a material. It is defined as the change in length divided by the original length. The formula for strain is given by:

Strain (ε) = Change in Length (ΔL) / Original Length (L)

Since we are given the original length (L) of each wire, and the compression is given as the change in length, we can calculate the strain using this formula.

Strain_copper = ΔL_copper / L_copper
Strain_steel = ΔL_steel / L_steel

c. Total elongation of both wires:
The total elongation of both wires can be calculated by summing up the individual elongations:

Total_elongation = ΔL_copper + ΔL_steel

Now, let's calculate the values numerically:

a. Stress in each wire:
Given:
Force applied (F) = 30 N
Young modulus of copper (E_copper) = 1.3 × 10^11 N/m^2
Young modulus of steel (E_steel) = 2.0 × 10^11 N/m^2

Using the formulas mentioned earlier, we can find the stress in each wire, considering the applied force and the calculated cross-sectional areas.

Stress_copper = F / A_copper
Stress_steel = F / A_steel

b. Strain in each wire:
Given:
Original length of copper wire (L_copper) = 1.50 m
Original length of steel wire (L_steel) = 1.20 m
Compression of each wire (ΔL_copper and ΔL_steel) = 20 mm = 0.020 m

Using the formulas mentioned earlier, we can calculate the strain in each wire.

Strain_copper = ΔL_copper / L_copper
Strain_steel = ΔL_steel / L_steel

c. Total elongation of both wires:
Given:
Compression of each wire (ΔL_copper and ΔL_steel) = 20 mm = 0.020 m

We can calculate the total elongation by summing up the individual elongations.

Total_elongation = ΔL_copper + ΔL_steel

Now you can substitute the given values and perform the calculations to find the answers.