Calculating Tension Ratios for Equilibrium of Identical Bodies

  • Thread starter kastamonu
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In summary, the conversation discusses the equilibrium of identical bodies with weight P and tension in ropes S1 and S2, and asks for the ratio of T1 to T2. The correct answer is 1/2, which is determined by considering the weight of K and the position of the pulley. The equilibrium conditions at nodes A and B are necessary for computing the solution.
  • #1
kastamonu
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Homework Statement



Identical K,L and M bodies with a weight of P are in equilibrium . If the tension in the rope S1 is T1 and S2 is T2, then what is the ratio T1/T2? (The picture is below)

Homework Equations


The Attempt at a Solution



T1 equals P. But I am stuck with T2. I cannot decide whether it is 2P or 3P. Do we have to add the weight of K to T2? If we add, it will be 3P.
 

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  • #2
S2 is the uppermost vertical string and so must support all of the weight. Its tension will be 3P.
 
  • #3
Then the answer is 1/3.But according to my book the answer is 1/2.
 
  • #4
the pulley is attached to a rigid support.T2 has a weight of 2P
 
  • #5
Let us call A the node above K and B the node above L. Let us assume that the angle between a horizontal line and the rope connecting A to B is 45 degrees (without this value you cannot compute a solution). Then you only have to write the equilibrium conditions at nodes A (first) and B (second).
The ratio is 1/2.
 
  • #6
Many Thanks
 

Related to Calculating Tension Ratios for Equilibrium of Identical Bodies

What is tension?

Tension is a force that is applied to an object in a way that causes it to stretch or compress. It is the opposite of compression, where forces push on an object inwards.

What are some common examples of tension?

Some common examples of tension include a rubber band being stretched, a rope being pulled taut, or a muscle being flexed in the body. Tension can also be seen in structures such as bridges and suspension cables.

How is tension measured?

Tension is typically measured in units of force, such as newtons. It can be measured using tools such as a spring scale or a force gauge.

What factors affect tension?

The amount of tension in an object is affected by several factors, including the force applied, the distance the object is stretched or compressed, and the material properties of the object, such as its elasticity and strength.

What are the practical applications of understanding tension?

Understanding tension is crucial in many fields, including engineering, physics, and biology. It allows us to design and build structures that can withstand tension forces, such as bridges and buildings, and also helps us understand the mechanics of the human body, such as how muscles and tendons work together to create movement.

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