## College Physics (4th Edition)

In order to break each rope, we need to apply a force to overcome the tensile strength of the rope. Since the tensile strength does not depend on the rope's length, the same force is required to break each rope. When we apply a force to a rope, the rope will stretch a certain distance before it breaks. We can write an expression for the distance $\Delta L$ that a rope stretches: $E = \frac{F/A}{\Delta L/L_0}$ $\Delta L = \frac{F~L_0}{A~E}$ We can see that the stretch distance is proportional to the original length $L_0$ of the rope. Since the longer rope stretches a greater distance before it breaks, we need to apply the force on the longer rope over a greater distance. Since energy is $force\times distance$, more energy is required to break the longer rope.