Find the maximum tension allowed.

In summary: So the only force is the 360N rope tension, which is balanced by gravity.In summary, in this problem, a man weighing 60 kg wants to safely climb a rope that is fixed at one end to a wooden clamp on the ground and passes over a tree branch, making a 30° angle with the ground. The maximum acceleration in the upward direction with which the man can climb safely is approximately 2m/s^2, assuming a gravitational acceleration of 10m/s^2 and neglecting friction at the tree branch. The wooden clamp can come out of the ground if an upward force greater than 360N is applied to it, but in this case, the only upward force is the tension in the rope
  • #1
SAUMYA B
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A light rope fixed at one end to the wooden clamp on the ground passes over a tree branch and hangs on the other side. It makes an angle 30° with the ground. A man weighing 60 kg wants to climb up the rope. The wooden clamp can come out of the ground if an upward force greater than 360N is applied to it. Find the maximum acceleration in the upward direction with which the man can climb safely. Neglect friction at the tree branch. Take g ≈ 10m /s^2.

Let t be tension in rope. Then upward force on the clamp is tsin30°≈t/2≈360N.
T≈720N
Let a be acceleration of man in upward direction then,
T-600N≈60 kg . a
Therefore maximun acceleration of the man is
a≈ (720-600)N/60 kg. ≈ 2m/s^2.


Now my question is if we draw the tree body diagram of the wooden clamp we should include the normal contact force by the rope and the ground.Therefore upward force on the clamp is the resultant of the of the normal contact force by the rope and the tension in it. Why then we only consider the tension in the rope as the only upward force.
 
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  • #2
From your description, it appears that the wooden clamp is thrust into the ground, and then the rope is tied to the clamp and thrown over a tree branch. I don't know what you mean by "the normal contact force by the rope and the ground."

Could you include a sketch of the problem?
 
  • #3
I think I understand the question. You are supposing that the clamp goes over the rope end, so a short horizontal section of rope is clamped between the ground below it and the clamp above it. Is that right?
But it could equally be that the clamp encompasses the rope and grips it perfectly well without needing any normal force from the ground.
Since there's no way to estimate what such a normal force would be in the first model, I think it's fair to take the second.
 

FAQ: Find the maximum tension allowed.

What is the maximum tension allowed?

The maximum tension allowed refers to the maximum amount of force or stress that a material or structure can withstand before breaking or failing.

How is the maximum tension allowed determined?

The maximum tension allowed is determined through various experiments and calculations, taking into consideration the material properties, design factors, and safety factors.

Why is it important to know the maximum tension allowed?

Knowing the maximum tension allowed is crucial in ensuring the safety and integrity of structures and materials, as exceeding this limit can result in catastrophic failures.

What factors can affect the maximum tension allowed?

Factors such as material type, composition, temperature, loading conditions, and environmental factors can all affect the maximum tension allowed for a particular material or structure.

How can the maximum tension allowed be increased?

The maximum tension allowed can be increased by using stronger or more durable materials, improving the design and construction methods, and implementing safety measures such as using tension-limiting devices or adding reinforcements.

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