Is my forces diagram correct? (static equilibrium problem)

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Discussion Overview

The discussion revolves around a static equilibrium problem involving a crane lifting a mass, where participants analyze a force diagram to determine the force acting on the crane's axis. The focus is on the application of Newton's laws and the geometry of forces.

Discussion Character

  • Homework-related
  • Technical explanation
  • Mathematical reasoning

Main Points Raised

  • The original poster (OP) presents a force diagram and seeks validation on its correctness for calculating the force R acting on the crane's axis.
  • One participant suggests simplifying the problem by focusing on the free body diagram (FBD) of the pulley and using Newton's first law in both x and y directions to find the components of the force R.
  • The OP indicates progress towards the solution but acknowledges discrepancies in the numerical results, particularly in calculating the components Rx and Ry.
  • Another participant points out potential errors in the OP's calculations, specifically in summing forces related to the weight and tension.
  • The OP expresses gratitude for assistance, attributing earlier mistakes to calculator errors.

Areas of Agreement / Disagreement

Participants generally agree on the approach to solving the problem, but the OP experiences uncertainty regarding the accuracy of their calculations and the resulting values for Rx and Ry. The discussion remains unresolved regarding the final numerical results.

Contextual Notes

There are indications of unresolved mathematical steps and potential miscalculations in the OP's approach, particularly concerning the application of trigonometric functions and the summation of forces.

Femme_physics
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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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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.
 
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?
 

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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...
 
Ah...it's that stupid calculator *embarrassed grin*...thanks a lot phantom :D What'd I do without you!
 
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:
 
Hehe... I love this forum. Best stuff on the internet!
 

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