Conservation of Mechanical Energy Problem

[smeagol]

This is something I am learning on my own. However, this problem is confusing me:

Red is a girl of mass m who is taking a picnic lunch to her grandmother. She ties a rope of length R to a tree branch over a creek and starts swing from rest at point A, which is a distance R/2 lower than the branch. What is the minimum breaking tension for the rope if it is not to break and drop Red into the creek?

What is this breaking tension thing? I don't quite understand what I am suppose to calculuate.

 

[himanshu121]

The Tension of the rope at the time of breaking will be zero.

Think why it Should be zero?

 

[ObsessiveMathsFreak]

I'll assume you've already calculated the tension on the rope for all points during red's swing.

What is the maximum value for this tension. Let's say it was 100N.

Now let's say that the breaking tension in the rope was 90N. this means that at 90N or more tension, the rope will snap.

So in order that red not plummet to her icy doom the breaking tension will have to be greater that the largest tension the rope expieriences during the swing.

 

[smeagol]

then there's no force pulling on the rope?

Also. How is there anywork done on this? the mass is accelerating toward the center, but movint tangent to the circle?

 

[Doc Al]

Originally posted by smeagol
What is this breaking tension thing? I don't quite understand what I am suppose to calculuate.

When the girl is at the bottom of the swing, she will have maximum speed and the tension in the string (if it doesn't break!) will be maximum.

You can find her speed at the bottom using conservation of energy.

Since she is moving in a circle, you can calculate what the force must be pulling her towards the center. And thus find what the tension in the rope must be. The "breaking tension" of the rope must be greater than the tension at the bottom, else the rope breaks. Make sense?