A steel cable with a radius of 1.5 cm supports a chairlift at a ski area. If the maximum stress is not to exceed 108 N m–2, what is the maximum load the cable can support ?
Solution and Explanation
Radius of the steel cable, r = 1.5 cm = 0.015 m
Maximum allowable stress = 10 8 N m - 2
Maximum stress = \(\frac{\text{Maximum force} }{\text{ Area of cross - section}}\)
∴ Maximum force = Maximum stress × Area of cross - section
= 108 × π (0.015)2
= 7.065 × 104 N
Hence, the cable can support the maximum load of 7.065 × 10 4 N.
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Concepts Used:
Stress Strain Curve
Stress:
The force applied per unit area in mechanics is understood as stress.
σ=FA
- σ is stress applied
- F is force applied
- A is that the area of force applied
- Stress is measured by unit N/m2
The ratio of internal force F that is produced when a substance is deformed, to the area A where force is applied is referred to as stress.
Strain:
Strain can be referred to as the ratio of the amount of deformation that the body experiences in the direction of force applied to the initial sizes of the body. The relation of deformation in terms of the length of the solid is shown below:
ε=δlL
where,
- ε = strain due to the stress applied
- δl = modified long
- L = the original length of the material
- Strain = the ratio for change of shape or size to the initial shape or size. It's expressed in numbers because it doesn't have any dimensions.
As strain defines the relative change in shape and it's a dimensionless quantity.
Explanation of Stress-Strain Curve:
The material's stress-strain curve delineates the connection between stress and strain for materials. In other words, a stress-strain curve is a graphical representation that shows the reaction of a material when a load is applied.