Calculating Tension & Reactions in an Unbalanced Pulley System

In summary, we are given an unbalanced pulley with a 6in radius of gyration and a 32.3 pound weight. A pair of 100pie.lb is applied to lift a weight of 96.6 pounds with an angular velocity of 3 rad/sec in the counter-clockwise direction. We are asked to determine the tension in the string, T, as well as the axial components of Ox and Oy for the reaction in O. Neglecting reaction friction and assuming a smooth periphery of the small pulley, the results are T=141.6 lb, Ox=-143.7 lb, and Oy=31.45 lb. In calculating these values, the equations of rigid body dynamics were
  • #1
skxnxr
2
0
Member warned that homework questions must include an effort

Homework Statement


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An unbalanced pulley 8in. radio. and 32.3 pounds weighing. It has a radius of gyration of 6in with respect to its axis. When a pair M = 100pie.lb applies, lifts a weight W = 96.6 pounds. In the position shown in the figure, the pulley has an angular velocity of 3 rad / sec in counter-clockwise. Determining the tension in the string T and axial components of Ox and Oy, of the reaction in O. Neglect reaction friction and suppose the periphery of the small pulley is smooth. Thanks

Book results:
T=141.6 lb
Ox=-143.7 lb
Oy=31.45 lb

Homework Equations

: (rigid body dynamics)[/B]
∑F=m.a
ΣT=(ri-R) x (mi ai)

The Attempt at a Solution


I try to raise the equations of rigid body dynamics, but I'm nowhere near the result. I think I have to take into consideration the imbalance of the pulley. How should raise the equations? Thanks
 
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  • #2
skxnxr said:
I try to raise the equations of rigid body dynamics, but I'm nowhere near the result.
Whether they are correct or incorrect, please show us what you have tried.
 
  • #3
I try this:
∑F=m.a
T - m.g = m.ay
T = m(ay + g)
T = 32,3 (ay + 32,2)
I need to calculate ay.

ΣT=IO.α
T.6in = IO.α
6T = (½ . m . r^2).α
6T=(½ . 32,3 . 6^2) . 3
T = 289. This result is not correct
 

FAQ: Calculating Tension & Reactions in an Unbalanced Pulley System

How do you calculate tension in an unbalanced pulley system?

In order to calculate the tension in an unbalanced pulley system, you will first need to identify all the forces acting on the system. Then, you can use Newton's laws of motion to set up and solve equations to find the tension in each segment of the pulley system.

What factors affect the tension in an unbalanced pulley system?

The tension in an unbalanced pulley system is affected by the weight of the objects being lifted, the angle of the pulleys, and the friction between the pulley and the rope. Additionally, any external forces acting on the system, such as wind or a person pulling on the rope, can also affect the tension.

How do you find the reactions in an unbalanced pulley system?

To find the reactions in an unbalanced pulley system, you will need to use the principles of static equilibrium. This means that the sum of all the forces acting on the system must be equal to zero, and the sum of all the torques (rotational forces) must also be equal to zero. By setting up and solving equations based on these principles, you can find the reactions at the different points of the pulley system.

Can the tension in an unbalanced pulley system ever be greater than the weight of the objects being lifted?

Yes, the tension in an unbalanced pulley system can be greater than the weight of the objects being lifted. This can happen when there is a person pulling down on the rope, or if there is a strong wind blowing against the objects. In these cases, the tension in the rope will need to be greater than the weight of the objects in order to keep them from falling.

What are some real-world applications of calculating tension and reactions in an unbalanced pulley system?

Calculating tension and reactions in an unbalanced pulley system is important in many real-world scenarios, such as construction, engineering, and physics research. For example, cranes use pulley systems to lift heavy objects, and engineers need to calculate the tension and reactions in these systems to ensure they can safely lift the weight. Additionally, understanding the tension and reactions in pulley systems can help scientists study the mechanics of movement in the human body, as our muscles and tendons function similarly to pulley systems.

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