Use the concept of impulse to explain the difference in the results of a jump using a proper bungee cord and a jump using ordinary rope.
(Ans: Is it that impulse is equal to mVf - mVi and the final velocity will be zero for the ordinary rope, however when using the bungee cord it is elastic, it prolongs the time it takes to reach the final velocity of zero hence making it safe for the bungee jumper. )
Is that correct?
Yes, you are partially correct. The concept of impulse can indeed be used to explain the difference in the results of a jump using a proper bungee cord and a jump using ordinary rope. However, there is a slight correction to be made to your explanation.
Impulse is defined as the change in momentum of an object and is calculated as the product of the force applied to the object and the time over which the force acts. In equation form, impulse (J) is equal to the final momentum (p_f) minus the initial momentum (p_i), which can be written as J = p_f - p_i.
With regards to the jumps, let's consider the jump using ordinary rope first. When a person jumps using an ordinary rope, the rope does not have any elasticity or ability to stretch, so it doesn't provide much resistance to the person's motion. As a result, when they reach the maximum point of their jump, the rope suddenly becomes taut and stops their motion abruptly. This sudden change in velocity results in a large change in momentum over a very short period of time. As a consequence, a large impulse is exerted on the person, leading to a significant force being applied to their body. This sudden force can be dangerous and can potentially cause injury.
On the other hand, when a person jumps using a proper bungee cord, the cord is designed to have elasticity or stretchiness. As the person jumps, the bungee cord starts to stretch and provides a resisting force that opposes their downward motion. This stretching of the bungee cord prolongs the time it takes for the person to come to a stop, thus increasing the time over which the force acts. As a result, the change in momentum and the impulse applied to the person are reduced compared to the ordinary rope jump. This gradual decrease in velocity and force makes it safer for the bungee jumper.
Therefore, the key difference between a jump using a proper bungee cord and an ordinary rope lies in the elasticity of the cord. The bungee cord allows for a more controlled deceleration and elongates the time over which the force is applied, reducing the impulse and potential for injury.