A 1200-kg car is being raised with a constant acceleration of 2.53 m/s² by a crane, using a 20-m long steel cable, 1.5 cm in diameter. Young's modulus for steel is 20 × 10¹⁰ N/m². What is the change in length of the cable? A) 8.4 mm B) 8.4 cm C) 4.9 mm D) 4.9 cm E) 4.9 m

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Quizplus · Accepted Answer

The change in length of the cable can be calculated using the formula for elongation: ΔL = (F * L) / (A * Y), where F is the force, L is the original length, A is the cross-sectional area, and Y is Young's modulus. The force F is the sum of gravitational force and the force due to acceleration: F = m(g + a). The cross-sectional area A = π(d/2)^2. Substituting the values, the change in length ΔL is approximately 8.4 mm.

A 1200-Kg Car Is Being Raised with a Constant Acceleration