What is the maximum tension in the rope?

In summary, a 75 kg student runs at 5 m/s and swings out over a lake, releasing the rope when his velocity is zero. Using the equation \LambdaKE = \frac{1}{2}mv_{f}^{2} - \frac{1}{2}mv_{o}^{2} = mgh, where m is the mass of the student and h is the height above the lake, we can calculate that the height at which the student releases the rope is approximately 1.276 meters. However, there is not enough information provided to determine the angle at which the rope is released or the tension in the rope before and after release.
  • #1
cyspope
27
0

Homework Statement


A 75 kg student runs at 5 m/s, grabs a rope, and swings out over a lake. He releases the rope when his velocity is zero. a) What is the angle when he releases the rope? b) What is the tension in the rope just before he releases it? c) What is the maximum tension in the rope?

Homework Equations


[tex]\Lambda[/tex]KE = [tex]\frac{1}{2}[/tex]mv[tex]_{f}[/tex][tex]^{2}[/tex] - [tex]\frac{1}{2}[/tex]mv[tex]_{o}[/tex][tex]^{2}[/tex] = mgh


The Attempt at a Solution



(75/2)*25 = 75 * 9.8 * h
h = 1.276

this is all I got.
 
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  • #2


Was this the exact wording of from the question? I don't quite understand what it meant. First, you wrote when he releases the rope, his speed is 0; if so, there would not be energy transfer to the rope from the running speed of the student. Also ,have you provided all the info?
 

What is the maximum tension in the rope?

The maximum tension in a rope is the greatest amount of force that can be applied to the rope without breaking it. It is an important factor to consider when designing structures or equipment that involve the use of ropes.

How is the maximum tension in a rope calculated?

The maximum tension in a rope can be calculated using the formula T = F/A, where T is the tension, F is the force applied to the rope, and A is the cross-sectional area of the rope. It is important to note that the maximum tension is affected by factors such as the type of material the rope is made of, its diameter, and its load capacity.

Can the maximum tension in a rope be exceeded?

Yes, the maximum tension in a rope can be exceeded, but doing so can result in the rope breaking or failing. It is important to always stay within the maximum tension limit to ensure the safety and functionality of the rope.

What are some common causes of high tension in a rope?

High tension in a rope can be caused by various factors, such as excessive weight or force being applied to the rope, sudden changes in direction or velocity, or improper use or maintenance of the rope. It is important to properly assess and manage these factors to prevent the rope from exceeding its maximum tension limit.

How can the maximum tension in a rope be increased?

The maximum tension in a rope can be increased by using a thicker rope with a higher load capacity, or by using multiple ropes in a system to distribute the load. However, it is important to always consider the limitations and safety factors of the rope and not exceed its maximum tension limit.

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