Question 13 of 13beginner🔧 ApplyNumerical3 marks

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?

Correct Answer

The maximum load the cable can support is approximately 7.07×107.07 \times 10⁴ N (or about 70.7 kN).

Exercise: EXERCISES | Q: 8.9
For More Understanding

Explanation

This question tests the understanding of the relationship between stress, force, and cross-sectional area. The formula Stress = Force/Area is used. Given the maximum permissible stress and the radius of the cable, we first calculate the cross-sectional area, then rearrange the formula to find the maximum force (load) the cable can withstand.

Solution Steps

  1. Step 1: Convert radius to SI units. Radius r = 1.5 cm = 1.5×101.5 \times 10⁻² m

  2. Step 2: Calculate the cross-sectional area of the cable. A = πr² = 3.14 × (1.5×101.5 \times 10⁻²)² = 3.14×2.253.14 \times 2.25 × 10⁻⁴ = 7.065×107.065 \times 10⁻⁴ m²

  3. Step 3: Apply the stress formula. Stress = Force/Area, therefore Force = Stress × Area

  4. Step 4: Calculate maximum load. F = 10⁸ N m⁻² × 7.065×107.065 \times 10⁻⁴ m² = 7.065×107.065 \times 10⁴ N ≈\approx 7.07×107.07 \times 10⁴ N

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