A Flexible chain between two hooks (statics)

In summary, two hooks at the same height hold a flexible chain weighing 41.0 N. The tangent to the chain at each hook makes an angle of 41.5° with the horizontal. The magnitude of force each hook exerts is 27.17 N, but this calculation is incorrect. The mistake may be in assuming the weight is distributed evenly and taking half of the weight for each hook. Further calculations are needed to determine the correct tension in the chain at its midpoint.
  • #1
pegasus24
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Homework Statement


A flexible chain weighing 41.0 N hangs between two hooks located at the same height. At each hook, the tangent to the chain makes an angle θ = 41.5° with the horizontal.
(a) Find the magnitude of the force each hook exerts on the chain.
(b) Find the tension in the chain at its midpoint.

Homework Equations


Fx = 0
Fy = 0
M = 0

The Attempt at a Solution


Let the magnitude of force each hook exerts be Rh.
Then Rh = Tsinθ = Wsinθ = 27.17 N
But this is wrong. What is my mistake in this calculation?
 

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  • #2
There are two hooks and assuming the weight is distributed evenly then how much of the weight is supported by each hook?
 
  • #3
I took the weight as 41/2 but the calculation is still wrong..
 

1. What is a flexible chain between two hooks?

A flexible chain between two hooks is a physical system in which a chain is suspended between two fixed points (hooks) and subjected to external forces. The chain is allowed to freely move and deform, while the hooks remain stationary.

2. What is the significance of studying a flexible chain between two hooks?

Studying a flexible chain between two hooks can help us understand the behavior of complex systems under external forces. It can also provide insights into the mechanics of materials and structures, as well as practical applications such as designing suspension bridges and analyzing the stability of hanging cables.

3. What factors affect the behavior of a flexible chain between two hooks?

The behavior of a flexible chain between two hooks is affected by several factors, including the length and weight of the chain, the distance between the hooks, the angle at which the chain is suspended, and the magnitude and direction of the external forces applied to the chain.

4. What are the different types of equilibrium states for a flexible chain between two hooks?

There are two types of equilibrium states for a flexible chain between two hooks: stable and unstable. In a stable equilibrium state, the chain hangs in a smooth curve between the hooks and any small disturbance will cause it to return to its original position. In an unstable equilibrium state, the chain forms a sharp kink and any small disturbance will cause it to fall off the hooks.

5. How can the equilibrium of a flexible chain between two hooks be calculated?

The equilibrium of a flexible chain between two hooks can be calculated using the principles of statics, which involve balancing the forces acting on the chain. This can be done by considering the weight of the chain, the tension in the chain, and the reaction forces from the hooks. Equations of equilibrium can then be used to solve for the unknown forces and determine the state of equilibrium for the chain.

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