Pendulum Projectile: Find Direction of Travel Formula

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Homework Help Overview

The discussion revolves around the dynamics of a pendulum and the implications of the string breaking at various positions. Participants are exploring how to determine the direction of travel of the pendulum bob upon release, particularly focusing on the geometry involved and the relationship between the pendulum's motion and the tangent line at the point of release.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants discuss the conditions under which the string might break and the resulting direction of travel. There are inquiries about finding the angle of the tangent line in relation to the axes influenced by gravity, as well as the relationship between the geometry of a pendulum and circular motion.

Discussion Status

The discussion is ongoing, with participants sharing their thoughts on the geometry of the pendulum's path and questioning the differences between circular motion and pendulum motion. Some have offered insights into the relationship between the angle of the tangent line and the position of the bob, but no consensus has been reached.

Contextual Notes

Participants express uncertainty about their geometric understanding and the implications of gravity on the pendulum's motion. There is a focus on the need for clarity regarding the tangent line's angle and its relation to the pendulum's position.

Jrlinton
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Homework Statement


This isn't a specific problem, I just wondering if there was a formula to describe the direction of travel an object would take if it was part of a pendulum and the string broke.

Homework Equations

The Attempt at a Solution


Seeing that if the string broke in the instant that the object was in its most downward position it would be released at an angle parallel to the horizontal and of it broke when the object was exactly 90 degrees from the resting position, it would travel straight up/down depending on where it was in its period, I would think that the direction of travel would be the tangent of the curve at that position? Is there is simplified equation for this?
 
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Jrlinton said:
would be released at an angle parallel to the horizontal and of it broke when the object was exactly 90 degrees from the resting position, it would travel straight up/down
You've got the hard part; the rest is ballistics.
 
Okay I guess what I'm confused about is how to find the angle of the tangent line in relation to the axes in a situation like a pendulum where the axes are dictated by gravity. So how would one find the angle of a tangent line and the origin as it relates to the position of the bob in motion.
 
So in other words the angle of the velocity and the horizontal.
 
Jrlinton said:
how would one find the angle of a tangent line
Is there a difference between the geometry of a pendulum and that of a circle?
 
I understand that. I guess my knowledge of circles is sub par. After drawing it up and unconfindently using what I could recall from geometry I figured the angle was equal to that of the angle between the position of the bob to the vertical?
 
How about "perpendicular to the radius?"
 
Bystander said:
Is there a difference between the geometry of a pendulum and that of a circle?

The path of a simple pendulum is not a circle
 
lychette said:
The path of a simple pendulum is not a circle
:wideeyed::nb):wideeyed::nb):wideeyed:
 

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