To find the shear stress in the spring wire, we can use the formula:

Shear stress = Load / (Wire diameter * Number of active coils * Spring index)

Given:
Load = 1200 N
Wire diameter = 7 mm
Spring index = 6

First, we need to calculate the number of active coils. The number of active coils can be calculated using the formula:

Number of active coils = Total number of coils - Number of inactive coils

Since it is a helical compression spring, the number of inactive coils is given by:

Number of inactive coils = (Wire diameter) / (Mean coil diameter)

The mean coil diameter can be calculated using the formula:

Mean coil diameter = Outside diameter - Wire diameter

Given:
Spring index = 6
Wire diameter = 7 mm

We can assume the outside diameter to be 7 times the wire diameter:

Outside diameter = Spring index * Wire diameter = 6 * 7 mm = 42 mm

Now we can calculate the mean coil diameter:

Mean coil diameter = Outside diameter - Wire diameter = 42 mm - 7 mm = 35 mm

Now we can calculate the number of inactive coils:

Number of inactive coils = Wire diameter / Mean coil diameter = 7 mm / 35 mm = 0.2

Since the number of inactive coils cannot be a decimal, we can round it up to 1. Therefore, the number of inactive coils is 1.

Now we can calculate the number of active coils:

Number of active coils = Total number of coils - Number of inactive coils = Total number of coils - 1

To find the total number of coils, we can use the formula:

Total number of coils = Spring index * Number of active coils

Given:
Spring index = 6
Number of active coils = Total number of coils - 1

We need to solve these two equations simultaneously to find the number of active coils:

Number of active coils = 6 * Number of active coils - 1

Simplifying the equation:

5 * Number of active coils = 1

Number of active coils = 1 / 5 = 0.2

Since the number of active coils cannot be a decimal, we can round it up to 1. Therefore, the number of active coils is 1.

Now we can calculate the shear stress:

Shear stress = Load / (Wire diameter * Number of active coils * Spring index)
Shear stress = 1200 N / (7 mm * 1 * 6)
Shear stress = 1200 N / 42 mm
Shear stress = 28.57 N/mm

Therefore, the shear stress in the spring wire is approximately 28.57 N/mm.