Solve Rotating Mass Tensions: Find Tup and Tlow

In summary, a mass connected to a vertical axle by two strings rotating with angular velocity w and making a 45 degree angle with the axle has tensions of Tup=sqrt(2)mg and Tlow=sqrt(2)mg, with Fcp=(mv^2)/r and v=wr being the relevant equations. The x-component of Fcp is not equal to the sum of the x-components of Tup and Tlow, as r in (mv^2)/r is not l but l/sqrt(2).
  • #1
Ironmely
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0

Homework Statement


A mass m is connected to a vertical axle by two strings of length l each making a 45 degree angle with the axle. Both the axle and mass are rotating with angular velocity w. Gravity is pointed downward. Find the tension in the upper string Tup and the tension in the lower string Tlow.
(clue: if lw^2= sqrt(2)g then Tup=sqrt(2)mg


Homework Equations



Fcp=(mv^2)/r
v=wr

The Attempt at a Solution


when considering the y-axis:
Tup/sqrt(2)= Tlow(sqrt) + mg
when considering the x-axis:
Tup/sqrt(2) + Tlow/sqrt(2)= Fcp
Tup/sqrt(2) + Tlow/sqrt(2)= mlw^2

add the equations and then solve for Tup

I think I'm making a mistake when looking at the x-axis, the tension must come from the centripetal force but I am wondering if I'm stating that correctly. I was also thinking about the x-components of Tup and Tlow adding only to the x-component of Fcp but Fcp should be pointed radially towards the axle and also be perpeniduclar to it so then x-component of Fcp is Fcp...Am I making a wrong assumption somewhere here?
Thank you
 
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  • #2
Oh, sorry, I figured it out, r in (mv^2)/r is not l but l/sqrt(2)
 

FAQ: Solve Rotating Mass Tensions: Find Tup and Tlow

1. What is rotating mass tension?

Rotating mass tension is the force generated by the rotation of a mass. It is commonly seen in machines and vehicles where rotating parts, such as wheels or engines, create tension that helps to keep the machine in motion.

2. What is the significance of finding Tup and Tlow in solving rotating mass tensions?

Tup and Tlow refer to the upper and lower limits of the rotating mass tension. These values are important in determining the maximum and minimum tension that a rotating mass can generate. By finding these values, engineers can ensure that the machine or vehicle is operated within safe and efficient tension levels.

3. How do you calculate Tup and Tlow?

Tup and Tlow can be calculated using the formula: T = I * α, where T is the tension, I is the moment of inertia of the rotating mass, and α is the angular acceleration. The upper limit (Tup) is calculated by using the maximum value of α, while the lower limit (Tlow) is calculated using the minimum value of α.

4. What factors can affect the rotating mass tensions?

The rotating mass tensions can be affected by various factors such as the rotational speed, mass of the rotating object, and the shape and size of the rotating object. Other factors include the friction between the rotating object and its surroundings, and external forces acting on the rotating object.

5. How can rotating mass tensions be managed and controlled?

To manage and control rotating mass tensions, engineers can use various techniques such as adjusting the mass, shape, or size of the rotating object, changing the rotational speed, and implementing lubrication or other methods to reduce friction. Regular maintenance and monitoring of the rotating object can also help to prevent excessive tension buildup.

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