What is the tension in the strings when the slender bar begins oscillating

Question (2) will require some trigonometry to find the angle at which the bar's center of mass reaches its highest position. The law of conservation of mechanical energy will not be useful for either problem. In summary, for the given scenario of a slender bar being suspended by two strings and then being knocked to rotate around the vertical axis, the equilibrium equations and conservation of mechanical energy cannot be used to find the tension in the strings and the rotation angle of the bar's center of mass. Dynamics and trigonometry will be needed for these calculations.
  • #1
Ayenyen
1
0

Homework Statement


There is a uniform slender bar which is suspended by two light inextensible strings and hangs in equilibrium. (if the mass and length of the bar are m and 2b )

Now, someone slightly knocks one end to make the bar rotate around the vertical axis with initial angular velocity ω0.

I want to know two things

(1) what is the tension in the strings when the slender bar begins to rotate?

(2) What is the rotation angle of the bar when the center of mass reaches its highest position?
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Homework Equations


[/B]
ΣF=0,ΣMG=0 equilibrium equations

ΔT=−ΔV Low of conservation of mechanical energy

The Attempt at a Solution



Can I use the equilibrium equations and conservation of mechanical energy for these problems?
 
Last edited:
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  • #3
Ayenyen said:

Homework Equations


[/B]
ΣF=0,ΣMG=0 equilibrium equations

ΔT=−ΔV Low of conservation of mechanical energy

The Attempt at a Solution



Can I use the equilibrium equations and conservation of mechanical energy for these problems?
Once the bar is set into rotation, the equilibrium equations are no longer valid. Question (1) will require application of dynamics.
 

What is the tension in the strings when the slender bar begins oscillating?

The tension in the strings when the slender bar begins oscillating depends on multiple factors such as the length and material of the strings, the mass of the bar, and the amplitude of the oscillation. A higher tension will result in a higher frequency of oscillation.

How does the tension affect the frequency of the oscillation?

The tension in the strings directly affects the frequency of the oscillation. As the tension increases, the frequency also increases. This is because a higher tension results in a faster restoration force, allowing the bar to oscillate more quickly.

What happens if the tension is too low?

If the tension in the strings is too low, the bar may not be able to oscillate at all. This is because the restoration force is not strong enough to counteract the force of gravity, causing the bar to remain stationary instead of oscillating.

Can the tension in the strings be adjusted?

Yes, the tension in the strings can be adjusted by either tightening or loosening the strings. This can be done by changing the position of the strings on the bar or by using a tensioning device.

Is the tension affected by external factors?

Yes, external factors such as temperature and humidity can affect the tension in the strings. As the temperature increases, the strings may expand and the tension may decrease. Similarly, high humidity can also cause the strings to stretch, resulting in a lower tension.

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