A heavy payload of mass 40 kg is to be lifted vertically from rest using a cable. The cable has a maximum breaking strength of 480 N . What is the minimum time required to lift the payload to a height of 9 m without snapping the cable? (Take g = 10 m s ⁻² )

Step-by-step solution

To find the minimum time, the payload must be lifted with the maximum possible upward acceleration. Let a_ max be the maximum safe upward acceleration. The forces acting on the payload are tension T upwards and weight mg downwards. Using Newton's second law for upward motion: T - mg = ma For maximum acceleration, the tension will be at its maximum limit, T_ max = 480 N . 480 - 40(10) = 40 a_ max 480 - 400 = 40 a_ max 80 = 40 a_ max a_ max = 2 m s ⁻² Now, apply the kinematic equation for constant acceleration to fin