Final answer:
To find the stress in the wire, we calculate the force applied (weight of the load converted to Newtons) and divide it by the wire's cross-sectional area. The stress in the wire is 1.03 x 10⁸ N/m².
Step-by-step explanation:
To calculate the stress in the wire, we need to use the formula for stress, which is the force applied divided by the area over which the force is distributed. The force applied is the weight attached to the wire, which can be found by multiplying the mass of the weight by the acceleration due to gravity (g = 9.81 m/s²).
First, convert the weight's mass from kilograms to Newtons (force):
25.5 kg × 9.81 m/s² = 250.155 N
Next, calculate the cross-sectional area (A) of the wire. Since the cross section is circular, use the formula A = πr², where r is the radius of the wire. Convert the diameter to meters and divide by two to get the radius:
0.557 mm = 0.000557 m
radius = 0.000557 m / 2 = 0.0002785 m
A = π × (0.0002785 m)²
Now we can calculate the area of the wire's cross-section:
A = 3.14159 × (0.0002785 m)² = 2.43 × 10⁻⁷ m²
Lastly, we find the stress (sigma) by dividing the force by the area:
stress = 250.155 N / (2.43 × 10⁻⁷ m²)
stress = 1.03 x 10⁸ N/m²
Therefore, the stress in the wire is 1.03 x 10⁸ N/m².