Final answer:
To determine stress, strain, and compression in a cylindrical metal, we use formulas involving force, area, Young's modulus, and original length, ensuring all measurements are in consistent units and all relevant forces are considered.
Step-by-step explanation:
To calculate the stress, strain, and compression of a vertical cylindrical metal subject to a load, we use principles from mechanics of materials. Stress is defined as the force per unit area, calculated using σ = F/A, where F is the force and A is the cross-sectional area of the cylinder. Strain is the deformation divided by the original length, given by ε = ΔL/L, where ΔL is the change in length and L is the original length. Compression is the decrease in length due to the applied load.
To find the stress, we use the formula σ = F/A. The cross-sectional area of a cylinder is A = πr², where r is the radius. Once we calculate the stress, we determine the strain using Hooke's Law, which states that stress is directly proportional to strain within the elastic limit of the material, σ = Eε, where E is Young's modulus. The compression ΔL is obtained by rearranging the formula for strain, ΔL = εL.
It is important to convert all measurements to consistent units, such as meters and newtons, to calculate properly. If any additional forces or loads not mentioned in the problem are present, such as the weight of the cylinder itself, they must be accounted for in the force balance.