A 1200-kg car is being raised at a constant speed by a crane, using a 20-m long steel cable, 1.50 cm in diameter. Young's modulus for steel is 20 × 10¹⁰ N/m². What is the change in length of the cable? A) 6.7 mm B) 6.7 cm C) 3.3 mm D) 3.3 cm E) 3.3 m

Question

Quizplus · Accepted Answer

The change in length of the cable can be calculated using the formula for linear deformation: ΔL = (F * L) / (A * Y), where F is the force (weight of the car), L is the original length of the cable, A is the cross-sectional area, and Y is Young's modulus. The force is the weight of the car (1200 kg * 9.8 m/s²), the area is π*(0.015/2)² m², and Young's modulus is 20 × 10¹⁰ N/m². Solving gives approximately 6.7 mm.

A 1200-Kg Car Is Being Raised at a Constant Speed