A person of mass 80 kg needs to slide down a vertical rope. The rope can withstand a maximum tension of 600 N before breaking. What is the minimum downward acceleration with which the person must slide to ensure the rope does not break? (Take g = 10 m s ⁻² )

Step-by-step solution

Let a be the downward acceleration of the person. The forces acting on the person are the gravitational force mg downwards and the tension T upwards. Using Newton's second law for downward motion: mg - T = ma To prevent the rope from breaking, the tension T must be less than or equal to the maximum breaking strength T_ max . T 600 N From the equation of motion, T = mg - ma . Therefore, mg - ma 600 Substitute the given values ( m = 80 kg , g = 10 m s ⁻² ): 80(10) - 80a 600 800 - 80a 600 200 80a a 200 80 a 2.5 m s ⁻²