A Level Physics Practice Exam

How is the speed gained by a detached hook affected by the stiffness of a rope?

1. Higher stiffness results in lower speed

2. Higher stiffness results in higher speed

3. Stiffness has no effect on speed

4. Lower stiffness results in variable speed

The correct answer is: Higher stiffness results in lower speed

The correct understanding lies in the relationship between the stiffness of a rope and the dynamics of how motion is transferred through it. When you consider a detached hook, which could be part of a system where forces are applied (like in a spring or a pulley system), the stiffness of the rope affects how much energy is stored and released during motion. When a rope is stiffer, it can resist deformation more effectively. This means that when a force is applied, the rope transmits that force more directly without absorbing as much energy in stretching. As a result, a stiffer rope can provide a faster transition of energy to the hook, allowing it to gain speed more rapidly. Conversely, a less stiff rope tends to stretch more under the same force, which can absorb more energy as potential energy accumulates in the deformation of the rope. This energy absorption leads to a less efficient transfer of energy to the hook, resulting in a lower speed gained. Therefore, higher stiffness indeed correlates with higher speed since the energy is transmitted more efficiently through the system.