Final answer:
To calculate the stretch of a steel cable, we can use Hooke's Law which states that the stretch of an elastic material is directly proportional to the force applied to it. The formula to calculate the stretch is (force * length) / (cross-sectional area * Young's modulus). Using this formula, we can calculate the stretch of the steel cable with a 120 kg ball hanging from it.
Step-by-step explanation:
To calculate the stretch of a steel cable, we can use Hooke's Law, which states that the stretch of an elastic material is directly proportional to the force applied to it. The formula to calculate the stretch is given by
stretch = (force * length) / (cross-sectional area * Young's modulus)
In this case, the force acting on the cable is the weight of the ball, which is 120 kg * 9.8 m/s² = 1176 N. The length of the cable is given as 6 m. The cross-sectional area can be calculated using the formula for the area of a circle (A = π * r²), where the radius is half the diameter. Therefore, the area is 0.0025 m / 2)² * π = 4.91 x 10^-6 m². Young's modulus for steel is typically around 2.0 x 10^11 N/m².
Plugging in the values into the formula, we get:
stretch = (1176 N * 6 m) / (4.91 x 10^-6 m² * 2.0 x 10^11 N/m²) ≈ 1.53 x 10^-5 m
Therefore, the stretch of the steel cable is approximately 1.53 x 10^-5 meters.