What Angle \(\phi\) Balances the Pulley in Static Equilibrium?

In summary: The answer is x = 50lb, y = 70lb, and \phi = 53.13 degrees.In summary, the problem involves a 50 lb weight supported by a wire attached to a pulley at point B. The pulley rests on wire ABC and the tension in wire ABC is 70lb. The goal is to determine the angle \phi necessary to keep point B in balance. To solve this, a free body diagram of the pulley is drawn and Newton's first law is used in the x and y directions to find the angle, which is calculated to be 53.13 degrees.
  • #1
msds1502
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Homework Statement


statics.jpg
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A 50 lb weight is supported by a wire attached to a pulley at point B. The Pulley rests on wire ABC. If the tension in wire ABC is equal to 70lb determine the angle [tex]\phi[/tex] necessary to keep point B in balance


Homework Equations


F=ks



The Attempt at a Solution



I Know there is some force acting from C to D. There is also some spring force acting from C to E. What I don't understand is how to model the FBD with the tension force ABC and 50lb weight at point C
 
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  • #2
msds1502 said:

Homework Statement


statics.jpg
(rotate picture 90 degree clockwise)
A 50 lb weight is supported by a wire attached to a pulley at point B. The Pulley rests on wire ABC. If the tension in wire ABC is equal to 70lb determine the angle [tex]\phi[/tex] necessary to keep point B in balance


Homework Equations


F=ks



The Attempt at a Solution



I Know there is some force acting from C to D. There is also some spring force acting from C to E. What I don't understand is how to model the FBD with the tension force ABC and 50lb weight at point C
The problem is asking for the angle [tex]\phi[/tex] when the pulley is in equilibrium. Draw a free body diagram of the pulley only. The weight is given and the tension in the rope on each side of the pulley is give. So use Newton's first law in the x direction and in the y direction, to solve for the angle.
 

FAQ: What Angle \(\phi\) Balances the Pulley in Static Equilibrium?

1. What is static equilibrium with spring?

Static equilibrium with spring refers to the state in which a spring is at rest and not experiencing any changes in its position or shape. This means that the forces acting on the spring are balanced, resulting in no net force and no movement.

2. How is static equilibrium with spring achieved?

Static equilibrium with spring is achieved by ensuring that the sum of all the forces acting on the spring is equal to zero. This can be done by adjusting the applied force, or by changing the position of the spring until it reaches a point where the forces are balanced.

3. What are the factors that affect static equilibrium with spring?

The factors that affect static equilibrium with spring include the applied force, the spring constant, the displacement of the spring, and the weight of the object attached to the spring.

4. How does the spring constant affect static equilibrium?

The spring constant, which is a measure of the stiffness of a spring, affects static equilibrium by determining how much force is required to displace the spring from its resting position. A higher spring constant means that more force is needed to achieve static equilibrium, while a lower spring constant requires less force.

5. What are some real-life applications of static equilibrium with spring?

Static equilibrium with spring is used in various applications, such as in the suspension systems of vehicles, in weighing scales, and in mechanical devices that require precise measurements and balance. It is also used in sports equipment, such as trampolines and pogo sticks, to provide a spring-like effect.

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