What is the force exerted by the rope?

  • Thread starter Thread starter pivoxa15
  • Start date Start date
  • Tags Tags
    Force Rope
Click For Summary

Homework Help Overview

The problem involves a scenario where a person, Jo, is bungy jumping, and the forces exerted by a rope modeled as an ideal spring are being analyzed. The context includes the mass of Jo, the spring constant of the rope, and the distance fallen before the rope exerts a force.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants discuss the forces acting on Jo when she is at rest and question the relationship between tension in the rope and her weight. Some suggest using conservation of energy to analyze the situation, while others clarify the distinction between being at rest and having no acceleration.

Discussion Status

The discussion is active, with participants exploring different interpretations of the forces involved and the energy transformations. Some have provided hints and clarifications, but there is no explicit consensus on the final force exerted by the rope.

Contextual Notes

Participants are considering the implications of the rope's elasticity and the energy conversion involved in the bungy jump scenario. There are references to external resources and similar problems for additional context.

pivoxa15
Messages
2,250
Reaction score
1

Homework Statement


Jo decides to try bungy jumping while on an overseas holiday. A rope that could be easily stretched was tied to her ankles and she jumped off a bridge high above a river. Model this as an ideal spring with a spring constant of 20N/m. Jo has a mass of 60kg and, after she jumps, her centre of mass falls vertically a distance of 12m before there is a force exerted on her by the rope.

When the rope reaches maximum extension Jo will be momentarily at rest. What is the upward force that the rope exerts on Jo?


Homework Equations


Assume g=10m/s^2


The Attempt at a Solution


When Jo is at rest there is a 600N force downward so the reaction is a tension force of 600N in the rope. This tension is the upward force that the rope exerts on Jo. But the answers suggested the force is 5.4*10^2N. How did they get that?
 
Physics news on Phys.org
When Jo is at rest, she is accelerating upwards, otherwise she would not "bounce" up again. So the force in the rope is greater than her weight.

Hint: use conservation of energy.
 
pivoxa:
Remember that "balance of forces" means "no acceleration", whereas "at rest" means "no velocity".

Do not confuse velocity and acceleration, nor the states when either of them has the value 0!
 
Last edited:
I get it now. It is a good problem since it uses many concepts. The person falls 12m without any external forces for a total time of 1.55seconds. The speed at the end of this fall is 15.5m/s with a total of 7200J. All this energy must be converted into elastic potential energy and the string is stretched by 26.83m (fairly elatic rope - can stretch for such a long length in reality?). This amounts to a total upward force of 536.7N exerted on Jo.
 

Similar threads

Monkey accelerating up and down a rope
  • · Replies 38 ·
2
Replies
38
Views
5K
Find tension of a rope and kinetic force
  • · Replies 13 ·
Replies
13
Views
3K
Velocity of a falling folded rope and reaction force
  • · Replies 10 ·
Replies
10
Views
3K
Tension in a rope at the midpoint
  • · Replies 8 ·
Replies
8
Views
9K
Tension force of block and rope
  • · Replies 25 ·
Replies
25
Views
6K
Force exerted on a pivot point of a rigid bar
  • · Replies 8 ·
Replies
8
Views
8K
What is the tension in the rope that connects the tugboat
  • · Replies 15 ·
Replies
15
Views
7K
How Do You Calculate Tension in Ropes Connecting Tugboat and Barges?
  • · Replies 1 ·
Replies
1
Views
4K
Girl on a swing, find tension and force
  • · Replies 32 ·
2
Replies
32
Views
12K
What is the tension and velocity in a rope attached to a moving space station?
  • · Replies 3 ·
Replies
3
Views
2K