Solving FBD with No Angle Given

  • Thread starter Saladsamurai
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In summary, the conversation discusses a problem involving a diagram with two springs and a pulley, where the unstretched length of each spring is given as 6 meters. The conversation also includes calculations using trigonometry to find the angles and forces involved in the problem. There is some confusion regarding the unstretched length of the springs, but it is ultimately determined that the unstretched length of each spring is actually 3 meters. The conversation ends with a resolution to the problem and a clarification of the unstretched length of the springs.
  • #1
Saladsamurai
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[SOLVED] FBD troubles

Homework Statement

Picture1.png


I am looking at 3-15 (with diagram). I am having trouble since there is no angle given.

I have so far [itex] -F+F_{ax}+F_{cx}=0[/itex] and in y direction [itex]F_{ay}=F{cy}[/itex].

Since the y components are equal, the springs have equal unstretched lengths, can I assume that the angle they make with the horizontal must be [itex]45^\circ[/itex]?

Or that since the vertical distance between the B and A must be 3 meters?
Or is this not the way to be looking at it?

Thanks,
Casey
 
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  • #2
Pythagoras is the simple answer here. you can split the diagram into 2 right angled triangles with side lengths d and 3m.
 
  • #3
You are given enough of the sides of the triangles formed by the pulley's (d is given to you in the problem) to find the angles and other sides of the triangles. You should be able to find all the angles you need just using trig. Take another look at the figure, and try to use trig and the Pythagorean theorem to find your angles and unknown sides.(Kurdt, you beat me to it! It was a close one though...)
 
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  • #4
Hint: Let be [tex]\theta[/tex] the angle that the springs make with the horizontal. Then:

[tex]\cos\theta=\frac{d}{\sqrt{d^2+9}}[/tex]

Bye!
 
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  • #5
Saladsamurai said:
Since the y components are equal, the springs have equal unstretched lengths, can I assume that the angle they make with the horizontal must be [itex]45^\circ[/itex]?

Or that since the vertical distance between the B and A must be 3 meters?
Or is this not the way to be looking at it?

Thanks,
Casey

Thanks guys. Could you answer my original question too? Is this why I have enough info^^? Since y components are equal and the springs are identical implies that the angle is bisected?

Thanks
 
  • #6
Yes, since the two springs have the same stiffnes and the same unstretched lengths, when you apply them a force, they stretched to the same length. Therefore they form an isoceles triangle.
 
  • #7
I am not sure what I'm doing wrong here. The hypoteneuse=3.354m then I should have the magnitude of the spring force as [itex]F_s=-ks=-500(3.354-6)=1323 N[/itex].
Then I have in the x direction for the applied force
[itex]F_A=F_s\cos\theta +F_s\cos\theta=2*1323\cos63^\circ=1.2kN[/itex]
But my answer key says 158 N

I got the angle from [itex]\arctan\frac{3}{1.5}=63.43^\circ[/itex]
 
  • #8
[tex]F_s=500(3.345-\bold{3})[/tex]

The length of each spring is 3m.
 
  • #9
It says in the problem statement each spring has an unstretched length of 6 m.
[itex]F_s=-ks=-k(l_f-l_o)[/itex]

Where are you getting 3? Thanks for the help so far by the way. :)
 
  • #10
Unstretched length of each spring is 3 m. Thereforer stretching is 3.354 - 3 = 0.354m. Now calculate the force.
 
  • #11
But the diagram shows that each spring has an unstretched length of 3 m. Maybe the statement is ambiguous...?

Moreover, in this case: [tex]l_f>l_o[/tex]
 
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  • #12
chuy said:
[tex]F_s=500(3.345-\bold{3})[/tex]

The length of each spring is 3m.

rl.bhat said:
Unstretched length of each spring is 3 m. Thereforer stretching is 3.354 - 3 = 0.354m. Now calculate the force.

Okay, maybe I was brainwashed or something but I'll ask again: WHERE do you see something that says the 'unstretched spring is 3 m'?

OP says length of unstretched spring=6 m

Thanks,
 
  • #13
chuy said:
But the diagram shows that each spring has an unstretched length of 3 m. Maybe the statement is ambiguous...?

Moreover, in this case: [tex]l_f>l_o[/tex]
I see your point chuy. I don't know why the statement says that, but this does get me the correct answer.

I'll take it up with the author!
 
  • #14
WHERE do you see something that says the 'unstretched spring is 3 m'? In the quote it is given that unstretched length of AB and BC is equal to 6 m. Then ,from the diagram, obviuosly unstretche length of each spring is 3 m.
 
  • #15
rl.bhat said:
WHERE do you see something that says the 'unstretched spring is 3 m'? In the quote it is given that unstretched length of AB and BC is equal to 6 m. Then ,from the diagram, obviuosly unstretche length of each spring is 3 m.

AH HA! Thank you, was taking that to mean EACH, but 6m means the COMBINED length of the TWO.

Thanks rl.bhat. Thanks chuy.
 

1. What is FBD and why is it important in physics?

FBD stands for free body diagram and it is a visual representation of all the forces acting on an object in a given system. It is important because it helps us understand the behavior of the object and how the forces are affecting its motion.

2. How do I solve FBD when there is no angle given?

To solve FBD with no angle given, you need to first identify all the forces acting on the object and their direction. Then, using Newton's laws of motion, you can set up equations and solve for the unknown variables.

3. What are the key steps in solving FBD with no angle given?

The key steps are: identifying all forces acting on the object, drawing a FBD with all forces labeled and their direction shown, applying Newton's laws of motion to set up equations, and solving for the unknown variables.

4. Can FBD be used for both static and dynamic systems?

Yes, FBD can be used for both static (objects at rest) and dynamic (objects in motion) systems. In both cases, it helps us analyze the forces acting on the object and understand its behavior.

5. What are some common mistakes to avoid when solving FBD with no angle given?

One common mistake is not properly labeling the forces or forgetting to include a force in the FBD. Another mistake is not considering all the forces acting on the object, including friction and normal forces. It is also important to double check the direction of the forces as it can affect the final solution.

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