If the rope in the system is not ideal (has stretch and elasticity), the tension in the rope during motion would become erratic and unpredictable.

Here's why:

• Ideal Rope vs. Non-ideal Rope:

  • An ideal rope is a theoretical concept where the rope is perfectly rigid and doesn't stretch or deform under tension. In such a scenario, the tension throughout the rope would be constant during motion.
  • A non-ideal rope, in reality, has some elasticity. It can stretch and store potential energy when pulled, and then release that energy as it contracts.

• Impact on Tension:

  • During motion, especially if the motion is rapid or involves sudden changes in direction or speed, the non-ideal rope will experience these variations in tension.
  • As the rope stretches, the tension will initially increase to resist the stretching force. However, as the rope reaches its limit of elasticity or experiences internal friction, the tension might fluctuate or even momentarily decrease.
  • When the stretching force is released, the rope might contract, causing the tension to momentarily spike before settling back down.

• Unpredictable Behavior:

  • Due to the complex interplay between stretching, contraction, and internal friction within the elastic rope, the tension throughout the length of the rope can become erratic and difficult to predict precisely.

Therefore, while the tension in an ideal rope would remain constant during motion, a non-ideal rope with elasticity would experience fluctuating and unpredictable tension values.