Max Speed & Acceleration for Climbing Rope

In summary, the maximum speed and acceleration with which a man can climb without breaking the rope depends on the weight of the man and the maximum tension the rope can withstand. If the rope can only hold 2/3 of the man's weight, he cannot climb up at all, but can slide down at a constant acceleration of 1/3 of his weight. However, if the length of the rope is given, the maximum speed cannot be determined.
  • #1
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If a man, weighing m1g is tryingting to climb up or down a rope, and the max tension T that the rope can withstand is 2m1g/3, then find the maximum speed and acceleration with which the man can climb without breaking the rope.

My work:
2m1g-m1g=m1a
=>a=-1g/3

doesn't this mean that the rope will break?
 
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  • #2
Apparrantly the man can not climb this rope. If he weighs w, and the rope can only hold (2/3)w, he can not even hang on to the rope, nevermind climbing it.

He can, however, slide down the rope at a constant acceleration of (1/3)w

BTW, "find the maximum speed" is nonsense for this problem unless the length of the rope is given.
 
  • #3
He can climb down the rope just by letting go- no tension at all!

As Chi Meson said, if the rope can only support 2/3 of the man's weight, he cannot climb up at all- he can't even hang on.
 
  • #4
thank you very much!
 

FAQ: Max Speed & Acceleration for Climbing Rope

What is the maximum speed for climbing rope?

The maximum speed for climbing rope depends on various factors such as the climber's technique, the type and condition of the rope, and the difficulty of the climb. Generally, experienced climbers can reach speeds of up to 10 feet per second, while beginners may climb at a slower pace of 5-7 feet per second.

How does the diameter of the rope affect its maximum speed?

The diameter of the rope can affect its maximum speed in two ways. A thinner rope will be lighter and easier to handle, allowing for faster movement. However, a thicker rope provides more friction and can be more durable, making it suitable for faster descents. Ultimately, the climber's preference and the type of climb will determine the ideal diameter for maximum speed.

Can the type of rope affect the acceleration for climbing?

Yes, the type of rope can significantly impact the acceleration for climbing. Dynamic ropes are designed to stretch and absorb the impact of falls, making them suitable for faster acceleration. On the other hand, static ropes do not stretch and are better for slow and controlled climbs.

Are there any techniques for increasing acceleration while climbing?

Yes, there are several techniques for increasing acceleration while climbing. These include using your legs to push off and propel yourself upwards, using your arms to pull yourself up, and using your weight to create momentum. It is essential to have proper technique and use your body's strength efficiently to increase acceleration.

How do factors like weather and altitude affect the maximum speed and acceleration for climbing rope?

Weather and altitude can significantly impact the maximum speed and acceleration for climbing rope. High altitudes can cause climbers to tire more quickly, affecting their speed and acceleration. Extreme weather conditions such as strong winds, rain, or cold temperatures can also slow down climbers and make it more challenging to maintain maximum speed and acceleration.

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