Finding Force on Rope: Trigonometry & Parameters

In summary, the homework asks the student to find the projection of a force over a rope as a function of the parameters given on the image. The student was not able to find the desired equation using trigonometry.
  • #1
Telemachus
835
30

Homework Statement


Hi there. Where, I got this exercise. I have a ball attached to an ideal rope with longitude L, moving on a circle with speed V on a circular trajectory with radius R over an horizontal plane.

So it asks me to express the subjected force over the rope as a function of the parameters given on the image below.
attachment.php?attachmentid=28779&stc=1&d=1286210320.png


So I thought of [tex]a_n=\dysplaystyle\frac{v^2}{R}[/tex], but the force given by this acceleration isn't the one I'm looking, right? I think I should use some trigonometry to find the projection of the force [tex]F=m*a_n[/tex] over the rope.

What you say?
 

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  • #2
What are the forces acting on the system? What is the net force in the horizontal direction in cases of uniform circular motion? If the ball stays at the same level, what is the net force in the vertical direction?
 
  • #3
I think I get it. In the horizontal direction I got the normal force, right? and in the vertical direction the weight. So the force projected on the rope will be the sum of the weight and the normal force.

Is that right? thanks for your answer.
 
  • #4
By normal force you're referring to the centripetal force?

The tension in the rope would be the vector sum of the forces in the x and y components. (You could also use Newton's laws to solve for each of the components, and then divide by the appropriate trigonometric function to get the magnitude of this tension force. This would probably lead to a "nicer" looking answer.)
 
  • #5
jhae2.718 said:
By normal force you're referring to the centripetal force?
Yes.

The tension in the rope would be the vector sum of the forces in the x and y components. (You could also use Newton's laws to solve for each of the components, and then divide by the appropriate trigonometric function to get the magnitude of this tension force. This would probably lead to a "nicer" looking answer.)
Lets see if I get it: [tex]F=m\dysplaystyle\frac{v^2}{R}i-mgj[/tex]

where i and j are the versors on the direction x and y respectively.
Is that right?
 
  • #6
That would give you the tension in the rope in vector form, if the positive x direction is taken to be toward the center of the circle.

By the way, you may want to write [tex]F[/tex] as [tex]\vec{F}[/tex] since it's in vector form. (In LaTeX, [tex]\hat{\imath}[/tex] is \hat{\imath} and [tex]\hat{\jmath}[/tex] is \hat{\jmath}.)
 
  • #7
Thank you very much :)
 

Related to Finding Force on Rope: Trigonometry & Parameters

1. What is the purpose of finding force on a rope using trigonometry and parameters?

The purpose of finding force on a rope using trigonometry and parameters is to determine the amount of force being applied on a rope in a given situation. This can be useful in various fields such as engineering, physics, and construction to ensure the safety and stability of structures.

2. What are the key parameters needed to find force on a rope?

The key parameters needed to find force on a rope are the angle of the rope, the tension in the rope, and the weight of the object being supported by the rope. These parameters can be measured or calculated using trigonometric functions.

3. How does trigonometry help in finding force on a rope?

Trigonometry helps in finding force on a rope by using the relationships between angles and sides in a right triangle. By applying trigonometric functions such as sine, cosine, and tangent, the unknown force can be calculated using known parameters.

4. Can finding force on a rope using trigonometry be applied to real-life situations?

Yes, finding force on a rope using trigonometry can be applied to real-life situations. For example, it can be used to determine the force needed to hoist a heavy object using a pulley system or to calculate the tension in a bridge's suspension cables.

5. Are there any limitations to using trigonometry to find force on a rope?

One limitation of using trigonometry to find force on a rope is that it assumes the rope and the forces acting on it are in an ideal, simplified scenario. In real-life situations, there may be other factors such as friction or non-uniform weight distribution that can affect the accuracy of the calculations.

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