First slide

Elastic behaviour of solids

Question

A steel cable with a radius of 1.5 cm supports a chair lift at a ski area. If the maximum stress is not to exceed 10⁸ N/m², what is the maximum load the cable can support?

Moderate

A

7 X10⁵ N
B

7 X10⁶ N
C

7 X10⁴ N
D

9 X10⁵ N

Solution

Given, radius of steel cable (r) =1.5 cm = 1.5 X 10^-2 cm
Maximum stress = 10⁸ N/m²
Area of cross-section of steel cable (A) = $π$ r²
$\begin{array}{l} = 3.14 \times {(1.5 \times 10^{- 2})}^{2} m^{2} \\ = 3.14 \times 2.25 \times 10^{- 4} m^{2} \end{array}$
$\begin{array}{l} Maximum stress = \frac{Maximum force}{Area of cross-section} \\ \begin{array}{l} Maximum force = Maximum stress \times Area of cross-section \\ = 10^{8} \times (3.14 \times 2.25 \times 10^{- 4}) N \\ = 7.065 \times 10^{4} N \\ = 7.1 \times 10^{4} N \end{array} \end{array}$

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