How to Solve for CosA and T in a Conical Pendulum?

In summary, the conversation discusses a problem involving a conical pendulum and finding the values of CosA and T using given variables such as V, m, g, and L. The speaker shares their solution and asks for help in presenting cosA without sinA. Another person suggests simplifying the equations and using the relationship between sin and cos to solve for T. The speaker expresses gratitude for the guidance.
  • #1
sAXIn
12
0
Hello all , I encouter a problem solving this one :

We are given a conical pendulum with : V - tan. speed of particle
m - mass of rotating particle
g - gravity acceleration
L - leght of the string

We need to find CosA , T by what is given above !
A- is the angle between the string and vertical line !

So : I wrote : tcosA=mg
tsinA=mv^2/R
R=LsinA

but I can't present cosA without sinA or something
Please Help !
 
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  • #2
sAXIn said:
So : I wrote : tcosA=mg
tsinA=mv^2/R
R=LsinA
That's fine. You can simplify and solve for T. Use the 3rd equation to eliminate R from the 2nd equation. Then realize that [itex]\sin^2\theta = 1 - \cos^2\theta[/itex].
 
  • #3
okay got it I get 2nd order eq.
thanks a lot
 

FAQ: How to Solve for CosA and T in a Conical Pendulum?

1. What is a conical pendulum?

A conical pendulum is a pendulum that moves in a circular arc on a plane instead of a straight line. It consists of a weight suspended by a string or rod that is attached to a fixed point at the top. The weight moves in a cone shape due to the combined forces of gravity and the tension of the string or rod.

2. How does a conical pendulum work?

A conical pendulum works by utilizing the principles of circular motion and gravity. The weight suspended by the string or rod acts as the centripetal force, pulling the weight towards the center of the circular motion. The tension in the string or rod acts as the restoring force, keeping the weight in its circular path.

3. What factors affect the motion of a conical pendulum?

The motion of a conical pendulum is affected by the length of the string or rod, the mass of the weight, the speed of the weight, and the angle at which the string or rod is suspended. These factors can change the centripetal force and the tension in the string or rod, leading to variations in the motion of the pendulum.

4. How is the period of a conical pendulum calculated?

The period of a conical pendulum can be calculated using the formula T = 2π√(L/g), where T is the period (time for one revolution), L is the length of the string or rod, and g is the acceleration due to gravity. This formula assumes a small angle of inclination and neglects the mass of the string or rod.

5. What are the applications of conical pendulums?

Conical pendulums have various applications in physics, such as demonstrating circular motion, measuring the acceleration due to gravity, and studying the relationship between tension and centripetal force. They are also used in some mechanical devices, such as centrifuges and gyroscopes, for their ability to maintain a constant circular motion.

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