Is my forces diagram correct? (static equilibrium problem)

In summary, the force R that acts on the axis of the crane (O), if the crane lifts in a constant speed a mass of 500 kg. The incline angle of the cable to the horizontal line is 45 degrees.
  • #1
Femme_physics
Gold Member
2,550
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(static equilibrium problem)

Homework Statement




Calculate the force R that acts on the axis of the crane (O), if the crane lifts in a constant speed a mass of 500 kg. The incline angle of the cable to the horizontal line is 45 degrees. Do not consider pulley friction.

The answers are:

R = 9063.23 [N]
Beta = 67.5 degrees

[PLAIN]http://img130.imageshack.us/img130/2276/forcesquest.jpg



The Attempt at a Solution



I've only made a force diagram to ask you guys whether it's correct.

[PLAIN]http://img339.imageshack.us/img339/7528/forces.jpg


*sighs* Truth is playing with triangles, law of Sines, and sum of all forces on X and Y is getting me nowhere -- but is this the way to solve it? I think that if my force diagram is correct it should be easy...just too many unknowns...
 
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  • #2
You are doing more work than necessary...the OP just wants the force applied at O, so draw a FBD of the pulley, note the tension in the rope, and use Newton 1 in the x and y directions to solve for Rx and Ry...and Pythagorus to solve for R. The direction of R must be along the bisector of the angle between the ropes.
 
  • #3
Well, I've taken your advice and I'm inching close to the answer in terms of the numerical result but still a bit off... it seems to make since though... (angle is a piece of cake once I have the correct Rx and Ry...clear I don't yet)

I attached the file of my new diagram and method to solve it...do you mind taking a look?
 

Attachments

  • 600pf.jpg
    600pf.jpg
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  • #4
Dory said:
Well, I've taken your advice and I'm inching close to the answer in terms of the numerical result but still a bit off... it seems to make since though... (angle is a piece of cake once I have the correct Rx and Ry...clear I don't yet)

I attached the file of my new diagram and method to solve it...do you mind taking a look?
Again your equations are good but your math is lousy :wink:. Add up mg and Tsin45 again...
 
  • #5
Ah...it's that stupid calculator *embarrassed grin*...thanks a lot phantom :D What'd I do without you!
 
  • #6
Dory said:
Ah...it's that stupid calculator *embarrassed grin*...thanks a lot phantom :D What'd I do without you!
Well,without me, you can always count on nvn or tiny-tim...and a host of others...:wink:
 
  • #7
Hehe... I love this forum. Best stuff on the internet!
 

FAQ: Is my forces diagram correct? (static equilibrium problem)

How do I know if my forces diagram is correct?

To ensure the accuracy of your forces diagram, make sure that all the forces acting on the object are correctly identified and drawn in the correct direction. Also, check that the forces are properly scaled and balanced according to Newton's Third Law.

What are the key components of a forces diagram?

A forces diagram should include the object being analyzed, all forces acting on the object, and arrows indicating the direction and magnitude of each force. It should also have a reference point or coordinate system to accurately represent the forces in 2D or 3D space.

Can a forces diagram be incorrect?

Yes, a forces diagram can be incorrect if any of the forces are missing, drawn in the wrong direction, or not properly scaled. It is important to double-check and revise the diagram as needed to accurately represent the forces acting on an object.

Are there any common mistakes in creating a forces diagram?

One common mistake is forgetting to include all the forces acting on the object, including friction or air resistance. Another mistake is not considering the direction and magnitude of each force accurately, as this can affect the overall equilibrium of the object.

How can I improve my forces diagram?

To improve your forces diagram, you can use a ruler to draw neat and accurate arrows for the forces. You can also label each force and use different colors to differentiate between them. Additionally, it is helpful to practice and check your diagram with the known laws and principles of physics.

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