Calculating Minimum Breaking Tension for Vine Rope Swing

In summary: Crazy, is this a torque or like.. centripital force question?.. or.. haha sorry I'm trying to learn too.This is a centripetal force question. You can use the following equations:F = maa = v^2/rKE is at a max at the bottom of the swing, PE is at a max at the starting point. so mgh = (1/2)mv^2.mv^2/R = F_c = 2mgsin(40)So the maximum force on the rope (at the bottom) is:F_{max} = mg + F_c = mg + 2mgsin(40
  • #1
b_phys28
2
0
A guy wishes to swing across a hole, using a vine rope. In order to reach the other side he must swing so that the rope makes a maximum angle of 40 degres to the vertical. Regarding the guy as an 85 kg point mass, what is the minimum breaking tension of the rope if the rope is not to break?
 
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  • #2
b_phys28 said:
A guy wishes to swing across a hole, using a vine rope. In order to reach the other side he must swing so that the rope makes a maximum angle of 40 degres to the vertical. Regarding the guy as an 85 kg point mass, what is the minimum breaking tension of the rope if the rope is not to break?
When the man is swinging, what are the forces on the rope? Where are they maximum? What are the forces on the rope at that point?

AM
 
  • #3
Crazy, is this a torque or like.. centripital force question?.. or.. haha sorry I'm trying to learn too.
 
  • #4
This is a centripetal force question. You can use the following equations:

F = ma
a = v^2/r

KE is at a max at the bottom of the swing, PE is at a max at the starting point. so mgh = (1/2)mv^2.

You can calculate the height, but you need the length of the rope to figure that out.

I can't really think of a way to do this without the length of rope. If you have it, just use trig, get the h, plug it in.
 
  • #5
dboy said:
This is a centripetal force question. You can use the following equations:

F = ma
a = v^2/r

KE is at a max at the bottom of the swing, PE is at a max at the starting point. so mgh = (1/2)mv^2.

You can calculate the height, but you need the length of the rope to figure that out.

I can't really think of a way to do this without the length of rope. If you have it, just use trig, get the h, plug it in.
I don't think you need the length of the rope. The PE is converted to KE at the bottom:

[tex]mgRsin(40) = PE = \frac{1}{2}mv^2[/tex]

[tex]mv^2/R = F_c = 2mgsin(40)[/tex]

So the maximum force on the rope (at the bottom) is:

[tex]F_{max} = mg + F_c = mg + 2mgsin(40) = mg(1 + 2sin(40))[/tex]

[tex]F_{max} = 85*9.8(1 + 2(.6428)) = 1903 N[/tex]

AM
 

Related to Calculating Minimum Breaking Tension for Vine Rope Swing

What is the purpose of calculating the minimum breaking tension for a vine rope swing?

Calculating the minimum breaking tension helps determine the maximum weight that the vine rope swing can safely hold without breaking. This is important for ensuring the safety of individuals using the swing.

What factors are involved in calculating the minimum breaking tension for a vine rope swing?

The main factors involved in calculating the minimum breaking tension are the material and thickness of the rope, the type of knot used, and the weight of the individual using the swing. Other factors may include environmental conditions such as temperature and humidity.

How do you calculate the minimum breaking tension for a vine rope swing?

The formula for calculating the minimum breaking tension is T = (M x g) / sin θ, where T is the minimum breaking tension, M is the weight of the individual, g is the gravitational acceleration, and θ is the angle at which the swing is hanging. The specific values for M, g, and θ can vary depending on the situation.

What are some potential safety concerns when using a vine rope swing?

Some potential safety concerns when using a vine rope swing include the potential for the rope to break under too much tension, the possibility of the knot slipping or coming untied, and the risk of falling or getting injured while using the swing. Calculating the minimum breaking tension can help mitigate these risks.

How can the minimum breaking tension be increased for a vine rope swing?

The minimum breaking tension can be increased by using a thicker and stronger rope, using a more secure and reliable knot, and reducing the weight placed on the swing. Regular maintenance and inspection of the rope and knot can also help ensure the safety and stability of the swing.

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