Final answer:
To calculate the tensile stress in a steel rod, we divide the weight of the supported load by the rod's cross-sectional area. The elongation caused by this stress is found by dividing the stress by Young's modulus and then multiplying by the original length. This illustrates the application of physics in understanding material behavior under load.
Step-by-step explanation:
Understanding Tensile Stress and Strain in Materials
When heavy loads are applied to materials such as steel rods, these materials experience a type of force known as tensile stress, which can cause them to elongate, also referred to as strain. To calculate the tensile stress in a rod, we use the weight of the load that the rod supports and the area over which this force is distributed. On the other hand, the elongation of the rod under this stress can be determined using the concept of Young's modulus.
To proceed with calculations, we need the following information:
- Mass of the hanging platform: 550 kg
- Gravitational acceleration (g): 9.81 m/s² (standard gravity)
- Cross-sectional area of the steel rod: 0.30 cm²
- Original length of the steel rod: 2.0 m
- Youth's modulus for steel (from reference data): 2.0 × 10¹¹ Pa
The force exerted by the platform due to gravity (weight) can be calculated as the product of mass (m) and the gravitational acceleration (g), F = m × g. This force, when applied to the cross-sectional area (A) of the rod, provides the tensile stress (σ):
σ = F / A
Using the weight of the 550-kg platform and the cross-sectional area of the steel rod, we can find the tensile stress exerted on the rod. To find the elongation, we rely on the equation that relates stress, strain (ε), and Young's modulus (Y):
σ = Y × ε
We can then solve this equation for strain, and multiply that value by the original length (Lo) of the steel rod to find the elongation (ΔL):
ε = σ / Y
ΔL = ε × L
o
The methodology described provides a step-by-step approach to assess and predict how materials will behave under tensile loads, essential for engineering and construction applications.