Torque Equilibrium and Elasticity problem

In summary, a 300 kg nonuniform boom is pinned at the pivot at P and has a 1000 kg block suspended from its end at A. The boom is supported by a 4.0 m long cable between points D and B and forms a 30° angle with the horizontal. The center of mass of the boom is at point C, 2.0 m from P. Using torques, the force of tension in the cable is calculated and used to find its x and y components, which are not the same as the force of the pivot. Further work is required to find the correct answer.
  • #1
Elysian
33
0

Homework Statement


A 300 kg nonuniform boom, 6.0 m long, is loosely pinned at the pivot at P. A 1000 kg
block is suspended from the end of the boom at A. The boom forms a 30° angle with
the horizontal, and is supported by a cable, 4.0 m long, between points D and B. Point
B is 4.0 m from P, and point D is 4.0 m above P. The center of mass of the boom is at
point C, which is 2.0 m from P. Find the tension in the cable, and the x- and
y-components of the force of the pivot on the boom.

http://img202.imageshack.us/img202/262/50669209.jpg

Homework Equations





The Attempt at a Solution



I calculated torques clockwise and counterclockwise and set them equal to each other, which are perpendicular so using the weight I solved for the Force perpindicular

(Fw(rod)*cos(30)*2)+(Fw(block)*cos(30)*6) = Ftcos(30)*4,

this gives me the Force of tension in the rope, from which i use to split into its X and Y components, and then I get the incorrect answer.

any help would be appreciated, thanks in advance
 
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  • #2
Hi Elysian,
You get the force of friction from your equation.
The next question is the x and y components of the force of the pivot. That force is not the same as the tension. Show your work in detail.

ehild
 

Related to Torque Equilibrium and Elasticity problem

1. What is torque equilibrium?

Torque equilibrium is a state where the net torque acting on an object is equal to zero. This means that there is no rotational acceleration and the object remains in a state of rest or constant rotational motion.

2. How is torque equilibrium different from force equilibrium?

Force equilibrium refers to a state where the net force acting on an object is equal to zero, resulting in no translational acceleration. On the other hand, torque equilibrium deals with rotational motion and requires the net torque to be zero for the object to remain in a state of rest or constant rotational motion.

3. What factors affect the torque equilibrium of an object?

The torque equilibrium of an object is affected by the magnitude and direction of the forces acting on the object, the distance of the forces from the axis of rotation, and the distribution of mass within the object.

4. How is elasticity related to torque equilibrium?

Elasticity refers to the ability of a material to undergo deformation and return to its original shape. In the context of torque equilibrium, elasticity becomes important when dealing with objects that can bend or twist, such as springs or beams. The amount of torque required to achieve equilibrium in these objects depends on their elasticity.

5. How can torque equilibrium be applied in real-life situations?

Torque equilibrium is a fundamental concept in physics and has many practical applications. It is used in the design of structures and machines to ensure stability and balance, such as in bridges and cranes. It is also important in sports, such as balancing a skateboard or performing stunts on a bicycle. In addition, torque equilibrium is crucial in understanding the mechanics of human movement, such as walking and throwing objects.

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