Pendulum speed given length and angle

Click For Summary

Homework Help Overview

The discussion revolves around a circular pendulum with a length of 1.2 m, which swings at an angle of 25 degrees to the vertical. Participants are tasked with predicting the speed of the mass at the end of the string using gravitational acceleration of 9.8 m/s².

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning, Problem interpretation, Assumption checking

Approaches and Questions Raised

  • Participants discuss the application of conservation of energy and the differences between circular and regular pendulums. There are attempts to derive speed using energy equations and considerations of rotational kinetic energy. Some participants express uncertainty about the correct approach and the role of centripetal force.

Discussion Status

Multiple interpretations of the problem are being explored, with some participants suggesting different methods and equations. Guidance has been offered to follow up on initial ideas, and there is an ongoing exchange of thoughts about the correct application of physics principles.

Contextual Notes

Participants are navigating assumptions about the pendulum's motion and the forces involved, with some noting the need for diagrams to clarify their understanding. There is also mention of previous attempts yielding different results, indicating a trial-and-error approach to the problem.

Kirasagi
Messages
9
Reaction score
0

Homework Statement


A circular pendulum of length 1.2 m goes around at an angle of 25 degrees to the vertical.

Predict the speed of the mass at the end of the string. Use g = 9.8 m/s2.

Answer in units of m/s

Homework Equations



1/2mv^2 = mgh
h = L - Lcosθ

The Attempt at a Solution



I used the above formula doing:
1/2mv^2 = mgh
v = √2g(L - Lcosθ)
Plug n' chug:
v = √2*9.8*(1.2 - 1.2cosθ)
v = 1.448 m/s

I've seen variations of this problem before, but I'm not really sure what I'm doing wrong.
 
Physics news on Phys.org
Kirasagi said:

Homework Statement


A circular pendulum of length 1.2 m goes around at an angle of 25 degrees to the vertical.

Predict the speed of the mass at the end of the string. Use g = 9.8 m/s2.

Answer in units of m/s


Homework Equations



1/2mv^2 = mgh
h = L - Lcosθ

The Attempt at a Solution



I used the above formula doing:
1/2mv^2 = mgh
v = √2g(L - Lcosθ)
Plug n' chug:
v = √2*9.8*(1.2 - 1.2cosθ)
v = 1.448 m/s

I've seen variations of this problem before, but I'm not really sure what I'm doing wrong.
What's the difference between a "circular pendulum" and a regular "pendulum"? The difference will make all the difference :smile:
 
Kirasagi said:
I used the above formula doing:
1/2mv^2 = mgh

How did you apply conservation of energy? :confused: There was an external force that made the pendulum start its circular revolutions from its initial state.

As I see the problem, the pendulum is revolving about the vertical axis. Drawing a diagram will help :smile:
 
To be honest I'm not really sure, I don't remember paying attention to pendulums too much. I'm assuming it also rotates/spins as it moves? Not sure what can I tie with that.

Am I doing this problem the right way? But having that idea, maybe I should add rotational kinetic energy?:

1/2mv^2 + 1/2IW^2 = mgh

W = v/r

Am I going on the right track?

Initially, another idea I had was to use centripetal force: mv^2/r, and using force diagrams.
 
Your initial idea was a good one. Follow it up!
 
The pendulum only revolves about the vertical axis.

Kirasagi said:
Initially, another idea I had was to use centripetal force: mv^2/r, and using force diagrams.

Try this out :smile:

Edit : somehow gneill is way faster!
 
Infinitum said:
How did you apply conservation of energy? :confused: There was an external force that made the pendulum start its circular revolutions from its initial state.

As I see the problem, the pendulum is revolving about the vertical axis. Drawing a diagram will help :smile:

I see, this was the way I saw it at first but I thought it's more complicated.

So:

Fx = Tsinθ = mv^2/r
Fy = Tcosθ = mg

T = mg/cosθ; plugging that in for Fx..
mv^2/r = mgtanθ, so..

v = √rgtanθ, where r = Length ? Not sure if I derived everything correctly.

Assuming I did everything right, final answer came to be v = 2.3417 m/s.. though I tried that a long time ago but got it wrong.
 
Kirasagi said:
...where r = Length ? Not sure if I derived everything correctly.

r is the radius of the horizontal circle where the pendulum is revolving. So, what component of the length will give you that?
 
Infinitum said:
r is the radius of the horizontal circle where the pendulum is revolving. So, what component of the length will give you that?

Would that be Lsinθ?

so

v = √g*Lsinθ*tanθ

v = 1.52234 m/s
 
  • #10
Kirasagi said:
Would that be Lsinθ?

so

v = √g*Lsinθ*tanθ

v = 1.52234 m/s

Yep!
 
  • #11
Got it right on my last try. Thanks!
 

Similar threads

Speed of ball on pendulum with Mechanical Energy
  • · Replies 9 ·
Replies
9
Views
1K
Maximum Angle of a Simple Pendulum with Given Parameters
  • · Replies 3 ·
Replies
3
Views
2K
For a Pendulum: Knowing Acceleration Find Maximum Angle
  • · Replies 26 ·
Replies
26
Views
4K
Uncertainty of pendulum period and pendulum length
  • · Replies 7 ·
Replies
7
Views
5K
Simulating a Rotary Inverted Pendulum in Python
  • · Replies 15 ·
Replies
15
Views
2K
Finding the distance of a peg so that a pendulum can circle around it
  • · Replies 2 ·
Replies
2
Views
1K
Foucault Pendulum at the North Pole
  • · Replies 9 ·
Replies
9
Views
3K
Pendulum Conservation of Energy
  • · Replies 31 ·
2
Replies
31
Views
4K
Max Impulse on a pendulum
  • · Replies 1 ·
Replies
1
Views
1K
How to find the maximum angle of a pendulum after a mass collides with it
  • · Replies 4 ·
Replies
4
Views
4K