What angle will the vine break and what's the max tension?

In summary, the question asks for the angle at which the vine will break when under 655 N of tension, and the maximum tension the vine can support for a 75.0 kg person to safely cross the river. The attempt at a solution uses the formula θ=cos^-1(T/mg) to find the angle, but does not include the v^2/r term in the equation. It is suggested to assume the starting angle of the vine is horizontal or to specify an initial angle, θ0, to express the answer in terms of.
  • #1
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Homework Statement


You come to a river and you see a vine you will use to swing across. Your mass is 75.0 kg, the vine is 18.0 m long, and the vine breaks when under 655 N of tension.
a) at what angle from the vertical will the vine break?
b) what should be the maximum tension supported by the vine for you to safely cross the river?

Homework Equations


T=mgcosθ+ m (v^2/r)
θ=cos^-1((T-m(v^2/r))/mg)
Tmax=mgcos(0)+m(v^2bottom/r)
Tmax=mg+m(v^2bottom/r)

The Attempt at a Solution


How i would solve this problem is by using the formulas like, θ=cos^-1(T/mg)
θ=cos^-1(655/((75.0kg)(9.8m/s^2))
and get θ=27.0 degrees

and Tmax=mg
Tmax=(75.0kg)(9.8m/s^2)
=735 N

is this the correct approach?
 
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  • #2
In your attempt, you have not included the v2/r term. To find the velocity you need to know what the starting angle is, but you do not have enough information. Is this the exact wording of the question? Is it possible you have left something out?
 
  • #3
haruspex said:
In your attempt, you have not included the v2/r term. To find the velocity you need to know what the starting angle is, but you do not have enough information. Is this the exact wording of the question? Is it possible you have left something out?

This is the EXACT wording of the question i have, this is on an old exam my professor gave the class to study from (without solutions). Am i supposed to assume since the most tenstion will be halfway thru the swing that it'll be 90 degrees? But it doesn't say he's starting with the vine exactly straight either so i feel that'd be incorrect to assume. Maybe he just wanted to keep the velocity term as v and solve and keep a v in the solution?
 
  • #4
Charlene said:
This is the EXACT wording of the question i have, this is on an old exam my professor gave the class to study from (without solutions). Am i supposed to assume since the most tenstion will be halfway thru the swing that it'll be 90 degrees? But it doesn't say he's starting with the vine exactly straight either so i feel that'd be incorrect to assume. Maybe he just wanted to keep the velocity term as v and solve and keep a v in the solution?
I think you will have to assume the vine starts horizontal. An alternative would be to specify an initial angle, θ0, and express the answer in terms of that.
 
  • #5
Deleted. I miss read the question.
 

1. What factors affect the angle at which a vine will break?

The angle at which a vine will break depends on several factors including the type and strength of the vine, the weight and force being applied to the vine, and the surrounding environmental conditions such as wind or obstacles.

2. Is there a specific angle at which all vines will break?

No, the angle at which a vine will break varies depending on the factors mentioned above. Each vine will have its own breaking point which can differ from other vines.

3. Can the tension on a vine be too high?

Yes, too much tension can cause a vine to break. It is important to carefully consider the weight and force being applied to the vine to avoid causing excessive tension.

4. How can the maximum tension on a vine be determined?

The maximum tension on a vine can be determined through experiments and calculations. Scientists can test the breaking point of different vines under varying conditions and use mathematical models to estimate the maximum tension that can be applied before the vine breaks.

5. Can the angle at which a vine breaks be predicted?

While it is difficult to predict the exact angle at which a vine will break, scientists can use their knowledge of the factors that affect vine breaking to make informed estimations. However, it is important to remember that the breaking angle can still vary due to unpredictable environmental factors.

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