Christian is making a Tyrolean traverse. That is, he 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. The rope must sag sufficiently so it won't break. Assume the rope can provide a tension force of up to 27kN before breaking, and use a "safety factor" of 10 (that is, the rope should only be required to undergo a tension force of 2.7kN ) at the center of the Tyrolean traverse.
Determine the distance x in meters that the rope must sag if it is to be within its recommended safety range and Christian's mass is 74.0kg.
If the Tyrolean traverse is incorrectly set up so that the rope sags by only one-fourth the distance found in part A, determine the tension force (in Newtons) in the rope.
Will the rope break?
repost that for me please
For anyone who is looking to solve this in the future:
First figure out the angle
F= 2Tsin(theta)-mg
where, F is total force, and here it must be zero to be at equilibrium
T=tension of rope (2.7kN)
mg=mass*grav= 9.8*74
then use Tan(theta) = Opposite/ Adjacent to figure out the length (Opp)
the angle should be under 10-ish, adjacent is 25/2. So your final answer is Opposite side= should be under 2 meters. Mine was 1.7M with slightly different values
Then for the second part, you divide the length (<2meters) by four. then find the new angle where one leg is 12.5 and the other is (length/4) =. you plug that angle into
0=2Tsin(theta)-mg and solve for T :)
My answer was around 10238 N
How do I do it exactly....
Christian is attempting to traverse a chasm by using a rope strung between two trees. The goal is to determine the distance that the rope must sag in order to be within the recommended safety range.
To calculate this, we need to consider the tension force that the rope can handle before breaking. In this case, the rope can withstand a maximum tension force of 27kN, but for safety purposes, we will use a safety factor of 10, which means the rope should only be required to undergo a tension force of 2.7kN.
To start, we can find the tension force at the center of the Tyrolean traverse. We know that the tension force at the center is equal to the weight of the person traversing the chasm plus the weight of the rope itself. The weight of the person can be calculated using the formula:
Weight = mass * gravity
Given that Christian's mass is 74.0kg, and assuming standard gravity of approximately 9.8 m/s^2, we can calculate the weight as follows:
Weight = 74.0 kg * 9.8 m/s^2
Next, we need to determine the weight of the rope. Since the problem does not provide the mass of the rope, we'll need to make an assumption or obtain that information from another source. Once we have the weight of the rope, we can add it to the weight of the person to find the total tension force at the center of the traverse.
Once we have the tension force at the center, we can consider the sag in the rope. The rope sags due to its own weight and the weight of the person. The sag can be calculated using the formula:
Sag = (Tension force at center / (2 * tension force per unit length)) - (distance between the trees / 2)
Given that the tension force per unit length is 2.7kN and the distance between the trees is 25m, we can substitute these values into the formula to find the sag in the rope.
Once we obtain the sag distance, we need to determine if it is within the recommended safety range. If it is within the safety range, the rope will not break. If it falls outside the safety range, it means the tension force in the rope exceeds its maximum capacity, and the rope may break.
If the Tyrolean traverse is incorrectly set up so that the rope sags by only one-fourth of the distance found in the previously calculated sag, we can determine the tension force in the rope using the same formula mentioned earlier:
Tension force = (2 * tension force per unit length * (sag / 4)) + (weight of person + weight of rope)
By plugging in the values, we can calculate the tension force in the incorrectly set-up rope.
To summarize:
1. Calculate the weight of the person using the formula Weight = mass * gravity.
2. Determine the weight of the rope (assuming it's known or obtained from another source).
3. Calculate the tension force at the center of the Tyrolean traverse by adding the weight of the person and the weight of the rope.
4. Calculate the sag distance of the rope using the formula Sag = (Tension force at center / (2 * tension force per unit length)) - (distance between the trees / 2).
5. Determine if the calculated sag distance falls within the recommended safety range.
6. If the Tyrolean traverse is set up incorrectly, calculate the tension force in the rope using the formula Tension force = (2 * tension force per unit length * (sag / 4)) + (weight of person + weight of rope).
By following these steps, we can find the answers to the given questions and determine if the rope will break in a given scenario.