Hinged rod attached to elastic string

Click For Summary
SUMMARY

The discussion focuses on a hinged rod of mass M and length L, attached to an elastic string with a natural length of L, which is fixed at point X and passes over a pin P located L distance from X. The Elastic Modulus of the string is defined as (1/4Mg). The total potential energy (PE) is derived as (1/4)MgL(1-cosθ-2sinθ), and the equilibrium angle θ is to be determined. Participants suggest using torque summation about point X and applying relevant trigonometric identities to solve the problem.

PREREQUISITES
  • Understanding of basic mechanics, specifically torque and equilibrium.
  • Familiarity with potential energy concepts in physics.
  • Knowledge of elastic properties and Elastic Modulus.
  • Proficiency in trigonometric identities and their applications.
NEXT STEPS
  • Study the principles of torque and equilibrium in rigid body mechanics.
  • Research potential energy calculations in elastic systems.
  • Learn about Elastic Modulus and its implications in material science.
  • Explore trigonometric identities relevant to physics problems.
USEFUL FOR

This discussion is beneficial for physics students, mechanical engineers, and anyone interested in the dynamics of elastic systems and torque analysis.

adam640
Messages
19
Reaction score
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.
 
Last edited by a moderator:
Physics news on Phys.org
How about summing torques about X to zero?

And then maybe an apposite trigonometric identity?
 

Similar threads

To find the modulus of elasticity of a light elastic string
  • · Replies 7 ·
Replies
7
Views
3K
To find the distance of a horizontally suspended rod from a ceiling
  • · Replies 2 ·
Replies
2
Views
2K
Ring attached to elastic and inextensible strings
  • · Replies 8 ·
Replies
8
Views
2K
To find the equilibrium position of a mass attached to an elastic string
  • · Replies 17 ·
Replies
17
Views
2K
Find the height to which a mass rises
  • · Replies 3 ·
Replies
3
Views
1K
Conservation of energy/Angular momentum for elastic collison
  • · Replies 5 ·
Replies
5
Views
2K
Resolving forces involving an elastic string
  • · Replies 1 ·
Replies
1
Views
2K
Finding the net elongation in a rod due to its own weight
  • · Replies 13 ·
Replies
13
Views
3K
Wave equation for an elastic rod
  • · Replies 3 ·
Replies
3
Views
2K
A falling rotating rod strikes a ball of mass M....
  • · Replies 13 ·
Replies
13
Views
2K