Understanding Tension in a Vertical Pendulum: Calculation and Explanation

  • Context: High School 
  • Thread starter Thread starter Joza
  • Start date Start date
  • Tags Tags
    Tension
Click For Summary

Discussion Overview

The discussion revolves around calculating the tension in the string of a vertical pendulum at various angles with respect to the vertical. Participants explore the forces acting on the pendulum bob and the application of Newton's laws to derive the tension under different conditions, including at the vertical position and at an angle.

Discussion Character

  • Exploratory
  • Technical explanation
  • Homework-related
  • Mathematical reasoning

Main Points Raised

  • One participant expresses confusion about calculating the tension in the string of a pendulum at an angle with the vertical.
  • Another suggests drawing a free body diagram and analyzing the forces acting on the bob, indicating that the sum of forces in both the X and Y directions should be considered.
  • A participant questions whether the sum of forces in the X direction can be zero if the pendulum is swinging, suggesting there is horizontal acceleration.
  • There is a reminder from a participant about previous discussions on the topic, emphasizing the need to identify forces and apply Newton's 2nd law, noting the presence of radial and tangential components of acceleration.
  • One participant describes their reasoning regarding the forces acting on the bob when the pendulum is at the vertical position, initially believing that tension and weight are equal in magnitude, which is later corrected by another participant.
  • A participant correctly identifies that the motion is circular and proposes an equation for the sum of forces in the Y direction, incorporating tension, weight, and centripetal acceleration.
  • Further discussion leads to the consideration of the pendulum's behavior at an angle, with hints provided to analyze force components and find speed.
  • There is a clarification that if the angle is at its maximum, the speed would be zero, but this is noted to be conditional based on the specific angle being discussed.

Areas of Agreement / Disagreement

Participants generally agree on the need to analyze forces and apply Newton's laws, but there are differing interpretations regarding the conditions under which tension and weight are equal, as well as the implications of the pendulum's motion at various angles. The discussion remains unresolved with multiple competing views on the calculations involved.

Contextual Notes

Participants express uncertainty about the correct approach to calculating tension, particularly regarding the conditions of motion and the effects of acceleration at different angles. There are also unresolved aspects concerning the specifics of the pendulum's motion and the assumptions made in the calculations.

Joza
Messages
139
Reaction score
0
I know this may sound very simple, but I am actually a bit confuses about it.

Say, in a pendulum swinging in a vertical plane. How does one calculate the tension in the string ( no mass) ,which is connected to a bob (mass m), at various points, say like and angle beta with the vertical?

I know its a very simple idea, but it is actually confusing me. I think I am doing it wrong. If someone could run thru it quickly, I mite see my mistake.

Cheers guys :redface:
 
Physics news on Phys.org
Draw a free body diagram of the bob. What forces are acting on it? The sum of all forces in X direction equals zero and like wise in Y direction. Once you derive the magnitude of the tension in X and Y direction, how would you calculate the magnitude of that vector?
 
Would the sum in x direction be zero since the pendulum is swinging? Isn't it acceleration in a horizontal direction?
 
Haven't we discussed this at length in your other thread?

I told you several times what to do. Did you try it?

(Also: Don't post the same question in multiple threads!)
 
This is actually a different question :redface:

It's a bit different but no matter how I try it my answer is wrong. I must be seriously flawed somewhere
 
I would not conclude that you were seriously flawed, but your approach may well be. :smile:

As always, identify the forces and apply Newton's 2nd law. Hint: The acceleration has a radial and a tangential component. Treat them separately.
 
Thanks, I'll try that in a second. But just to give you an idea of my reasoning, say the pendulum passes through the vertical.

My diagram says there are 2 forces on the bob, weight acting down, and tension in string acting upward. And these 2 should be equal in magnitude. Is THIS right?
 
Joza said:
My diagram says there are 2 forces on the bob, weight acting down, and tension in string acting upward.
This is right.
And these 2 should be equal in magnitude.
This is wrong.

Hint: What's the acceleration? Hint 2: What kind of motion is this?
 
Circular?

So my equation for the sum of y forces would be:

T - mg = (m(v)^2)/R ??
 
  • #10
Right!
 
  • #11
Hoorah! :rolleyes:

Ok so that's for the vertical position, and it seems straight forward, I just forgot about the acceleration. But what about say at an angle theta with the vertical?
 
  • #12
Analyze force components parallel to the string. Apply Newton's 2nd law. (Sound familiar?) Hint: Find the speed.
 
  • #13
But if that angle is its maximum, won't speed be zero?
 
  • #14
Joza said:
But if that angle is its maximum, won't speed be zero?
Sure, if the angle is the maximum angle. (But you just said angle theta. :wink:) I trust you can solve your earlier problem now?
 

Similar threads

High School Slack vs tight rope at the start of a pendulum
  • · Replies 8 ·
Replies
8
Views
2K
Graduate Time Average Value of Pendulum String Tension
  • · Replies 34 ·
2
Replies
34
Views
4K
High School Effect of mass on the acceleration of an elastic pendulum?
  • · Replies 3 ·
Replies
3
Views
1K
High School Analysis of Simple Pendulum Motion
  • · Replies 2 ·
Replies
2
Views
1K
Undergrad Pendulum Tension Force -- How to calculate the full vector?
  • · Replies 39 ·
2
Replies
39
Views
6K
High School Rotational Dynamics: Confused about the tension in this string pulling a mass up an incline
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad On whether the motion of a Foucault pendulum bob is comparable to ballistics
  • · Replies 10 ·
Replies
10
Views
3K
High School Sign conventions in torque and non-uniform circular motion
  • · Replies 1 ·
Replies
1
Views
2K
High School Calculating g with a Conical Pendulum
  • · Replies 3 ·
Replies
3
Views
4K
Undergrad Pendulum's Tension using Force reasoning and Newtons 3rd Law.
  • · Replies 2 ·
Replies
2
Views
2K