Final answer:
To calculate the force required to stretch a steel piano wire by 8.00 mm, Hooke's Law is used, where the force is directly proportional to the extension applied to the wire. The spring constant, determined by the wire's modulus of elasticity and cross-sectional area, is also necessary to perform an accurate calculation.
Step-by-step explanation:
The question asks to calculate the force required to stretch a steel wire, specifically a piano wire. A similar example would involve considering the force a piano tuner applies to stretch a steel piano wire by 8.00 mm, given its original length of 1.35 m and diameter of 0.850 mm. To solve this, one might use Hooke's Law, which describes the elasticity of materials and states that the amount of force (F) required to produce an extension (x) in a spring (or wire in this case) is directly proportional to that extension. This is expressed as F = kx, where k is the spring constant, which depends on the material's properties (Young's modulus) and geometry (cross-sectional area and original length).
To calculate the force in a real-world scenario, additional details such as the steel wire's modulus of elasticity and its cross-sectional area would be needed. This calculation would help us derive the wire's spring constant. In practical applications, like piano tuning or supporting a tightrope walker, this understanding is crucial for maintaining the tension that ensures the proper tone in an instrument or the safety and stability of the wire.