With what minimum acceleration can a fireman slide down a rope while breaking strength of the rope is 2 3 of the weight?

Step-by-step solution

Let m be the mass of the fireman and g be the acceleration due to gravity. The weight of the fireman is W = mg . The breaking strength of the rope is given as T_ max = 2 3 mg . When the fireman slides down with an acceleration a , the equation of motion is mg - T = ma , where T is the tension in the rope. To prevent the rope from breaking, the tension T must not exceed T_ max . Thus, T 2 3 mg . Substituting the maximum tension into the equation of motion: mg - 2 3 mg = ma . Solving for a : 1 3 mg = ma , which gives