Final answer:
The period of a swing increases if the length of the rope is extended due to the direct relationship between the pendulum's period and the square root of its length.
Step-by-step explanation:
If the length of the rope on a swing gets longer, the period of the swing will increase. This is because the period of a pendulum is proportional to the square root of its length. According to the formula T = 2π(√(L/g)), where T is the period, L is the length of the pendulum (rope length), and g is the acceleration due to gravity, an increased rope length results in a longer period for a complete oscillation. Hence, a longer rope means the swing takes more time to complete one back and forth movement.
Moreover, if you increase the length of the rope, would you have to apply more or less force to maintain the same speed? More force is required because the required centripetal force is inversely proportional to the radius—the length of the rope in this case—of the circular motion for a given mass and velocity.