Hinged rod attached to elastic string

In summary, the conversation discusses a rod with mass M and length L, hinged at point X and attached to end Y by an elastic string passing over a pin P. The natural length of the string is L, and P is a distance L from X. The elastic modulus of the string is (1/4Mg). The conversation then references GPE to X and seeks to prove that the total potential energy is (1/4)MgL(1-cosθ-2sinθ) and to find the angle θ for the equilibrium position. One suggestion is to sum torques about X and use a trigonometric identity.
  • #1
adam640
19
0
A rod (mass M, length L) hinged at point X. End Y is attached to X by an elastic string passing over a pin P, the natural length of the string is L. P is a distance L from X.

Elastic Modulus of string: (1/4Mg)

Refer to GPE to X and prove that total PE is: (1/4)MgL(1-cosθ-2sinθ) and find angle θ for the equilibrium position.

http://img155.imageshack.us/img155/1247/47349211.png

I literally have no idea where to begin with this and any help at all would be greatly appreciated.

Thank you in advance.
 
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  • #2
How about summing torques about X to zero?

And then maybe an apposite trigonometric identity?
 

1. What is a hinged rod attached to an elastic string?

A hinged rod attached to an elastic string is a simple mechanical system consisting of a rod or bar that is connected to an elastic string at one or both ends. The rod is able to rotate around the hinge, while the elastic string provides tension and allows for movement.

2. How does a hinged rod attached to an elastic string work?

The elastic string in a hinged rod system acts as a restoring force, meaning it pulls the rod back to its original position when it is displaced. This creates an oscillating motion in the rod, which can be harnessed for various purposes such as measuring forces or creating simple machines.

3. What are the applications of a hinged rod attached to an elastic string?

Hinged rods attached to elastic strings are commonly used in physics experiments to study the principles of oscillation and measure forces. They can also be used in simple machines such as catapults, trebuchets, and pendulums.

4. How do you calculate the period of oscillation for a hinged rod attached to an elastic string?

The period of oscillation for a hinged rod system can be calculated using the equation T = 2π√(I/mgd), where T is the period, I is the moment of inertia of the rod, m is the mass of the rod, g is the acceleration due to gravity, and d is the distance between the hinge and the center of mass of the rod.

5. What factors affect the oscillation of a hinged rod attached to an elastic string?

The oscillation of a hinged rod system can be affected by factors such as the length and stiffness of the elastic string, the mass and shape of the rod, and the angle at which the rod is released. Additionally, external factors such as air resistance and friction can also impact the oscillation of the system.

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