Final answer:
To find the force causing the stress in the wire, multiply the given stress (2 × 10⁷ N/m²) by the cross-sectional area after converting it to square meters (1.5 × 10⁻⁶ m²), resulting in a force of 30 N.
Step-by-step explanation:
The student is asking about the calculation of force given the stress and cross-sectional area of a metallic wire.
Stress is defined as force per unit area, and can be expressed with the formula σ = F/A, where σ is the stress, F is the force, and A is the area.
To find the force causing the stress, you need to rearrange the formula to solve for F: F = σ × A.
In this example, the stress σ is given as 2 × 10⁷ N/m², and the cross-sectional area A is 1.5 mm² which needs to be converted to m² for consistency in units.
Therefore, A = 1.5 × 10⁻⁶ m² (since there are 10⁶ mm² in 1 m²).
Then, the force F can be calculated by multiplying the stress by the converted area:
F = (2 × 10⁷ N/m²) × (1.5 × 10⁻⁶ m²) = 30 N.
This is the force causing the stress in the wire.