# How to find distance that the rope must sag

• kylenic1997
In summary, the conversation was about a homework question regarding a person named Bob traversing a chasm with a rope. The given information included the maximum allowable tension of 2900N, Bob's mass of 52.0kg, and the equation ma=∑F. The main question was how to calculate the distance x that the rope must sag at a point halfway across to stay within the recommended safety range. After some discussion and calculations, the person asking for help was able to find the answer, with the help of the other person providing guidance.
kylenic1997
Moved from technical physics section, so missing the homework template
I'm stuck on a homework question. It states, "Bob traverses a chasm by stringing a rope between a tree on one side of the chasm and a tree on the opposite side, 25 m away. Assume the rope can provide a tension force of up to 29 kN before breaking, and use a "safety factor" of 10 (that is, the rope should only be required to undergo a tension force of 2.9 kN). Bob's mass is 52.0 kg . Determine the distance x that the rope must sag at a point halfway across if it is to be within its recommended safety range."

The given information:
T=2900N
m=52.0Kg
and the equation I am using is ma=∑F, which is ma=T-mg

I'm not sure how to post my free body diagram, but I know that I am trying to find the sin of θ when i connect the two tension forces. This is where I'm stuck. I don't know how to get the value of the angle from only knowing the length of one side.

Any help is appreciated,
thank you

See the "upload" button to post a picture.

kylenic1997 said:
I don't know how to get the value of the angle from only knowing the length of one side.

You have to work out sin θ from the max allowable tension not the length of sides, that comes later. Post your free body diagram and equations for the vertical equilibrium.

kylenic1997
I was only using ma=∑F so far. Since it it is not accelerating i worked the equation into: 0=2Tsinθ-mg.
Plugging in the information given it should be (52.0Kg)(9.8m/s^2)=2(2900N)sinθ.
Which would make sinθ=.087862069, but I don't think this is correct since it doesn't have any units

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kylenic1997 said:
I was only using ma=∑F so far. Since it it is not accelerating i worked the equation into: 0=2Tsinθ-mg.
Plugging in the information given it should be (52.0Kg)(9.8m/s^2)=2(2900N)sinθ.
Which would make sinθ=.087862069, but I don't think this is correct since it doesn't have any units
The sine of an angle is not supposed to have any units.

You do have to take the sine of the angle and figure the tension in the rope with it.

So would the tension in this rope be found by multiplying 2900Nsinθ since that should give me the y value for the rope?

kylenic1997 said:
So would the tension in this rope be found by multiplying 2900Nsinθ since that should give me the y value for the rope?
I misspoke earlier. 2900 N is the allowable tension in this rope, once the factor of safety is accounted for.

What you need to find is the allowable sag in this rope such that the allowable tension of 2900 N is not exceeded. Use the sine of the angle to do that.

kylenic1997
So the tension should be (.5)(52.0kg)(9.8m/s^2)sinθ, which equals 22.38725518. I'm unsure about the units since it would still be in Newtons and not meters. Am I missing a step to change it to meters?

No that's not correct (wrong track. You already know the tension is 2900N).

Earlier you complained you couldn't calculate the dimensions of the triangle with just one side. Now you have a side and an angle.

kylenic1997
Ok so the length of the known side is 12.5m. To find the other side I use 12.5msinθ which gives me 1.098275863m. Is this correct?

## 1. How do I calculate the distance that a rope must sag?

To calculate the distance that a rope must sag, you will need to use the formula: d = (L/2) * (1 - cosθ), where d is the distance, L is the length of the rope, and θ is the angle of sag.

## 2. What is the purpose of finding the distance that a rope must sag?

The distance that a rope must sag is important for various applications such as bridge construction, zip lines, and suspension systems. It helps ensure that the rope is strong enough to support the weight and tension applied to it.

## 3. How do I measure the angle of sag for a rope?

The angle of sag can be measured using a protractor or by using trigonometric functions if the length of the rope and the height of the sag are known. In some cases, the angle can also be estimated visually.

## 4. Is the distance that a rope must sag the same as its length?

No, the distance that a rope must sag is not the same as its length. The length of the rope is measured from one end to the other, while the distance of sag is the distance between the lowest point of the rope and a straight line connecting the two ends.

## 5. What factors can affect the distance that a rope must sag?

The distance that a rope must sag can be affected by various factors such as the weight and tension applied to the rope, the type and thickness of the rope, and environmental conditions such as temperature and wind. It is important to consider these factors when calculating the distance of sag for safety and accuracy purposes.

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