What a I doing wrong? Swing/pendulum Questioj

  • Thread starter dantechiesa
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In summary, the conversation involves a discussion about a homework problem involving a swing with a given amplitude and period. The participants discuss the equations and methods used to calculate the speed at the bottom of the swing, and whether or not the given period is accurate. They also consider the possibility of the swing being a simple harmonic oscillator and how that may affect the solution. Ultimately, it is suggested to use the amplitude and period to find the maximum speed, and the need for more information about the pendulum length is mentioned.
  • #1
dantechiesa
apologies for the misspellings in the title, typed on my phone.

1. Homework Statement
You are in a swing in which the seat is 3.30 m from the suspension bar. You have managed to get the amplitude of your motion up to 2.05 m. If the period of your swing is 3.65 s, what is your speed when you are the bottom of your swing? Give your answer in km/h.

Homework Equations


mgh = .5mv^2[/B]

The Attempt at a Solution


The length of the swing: 3.3, with an ampltiude of 2.05.
Therefore we can calculate the height the swing achieves,
square root ( 3.32 - 2.052)
This gives roughly 2.586 (which I left un rounded in the calculator)
3.3 - 2.586 gives the height the swing achieves = ~.7139 (again, left unrounded)

Then I calculated the velocity using mgh = .5mv2

m(9.8)(.7139) = .5mv2
m's cancel

square root (9.8* .7139 / .5) = 3.74 m/s, which I then changed to 13.5 km/hr (which is my final answer unrounded)

This answer is incorrect and i can't figure out why.
 
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  • #2
If you were on a swing and managed to "get your amplitude up to 2.05 m" what would that mean? That you've reached a height of 2.05 m, or that the distance along the arc is 2.05 m? I honestly don't know, but either way it seems the way you've calculated the height can't be right.
 
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  • #3
Another thing you might think about is whether or not the swing is a simple harmonic oscillator. Hint, they give you the period!
 
  • #4
I've got nothing, is there anything you can give me to point me in the right direction?

All we have learned in SHM, no equation relates the velocity and amplitude/period, nor is there anyway to find height.
 
  • #5
Mister T said:
Another thing you might think about is whether or not the swing is a simple harmonic oscillator. Hint, they give you the period!
With that amplitude, it isn't. The period doesn't really help.
 
  • #6
Mister T said:
reached a height of 2.05 m,
It could not be that. Amplitude is the magnitude of displacement each way from some central position, so a total range of 4.1m.
Horizontal displacement does seem the most likely interpretation, but it might be worth trying arc length.
 
  • #7
haruspex said:
With that amplitude, it isn't. The period doesn't really help.

Well, realistically, yes. But if you want to be realistic the given period wouldn't be correct, would it?
 
  • #8
dantechiesa said:
I've got nothing, is there anything you can give me to point me in the right direction?

All we have learned in SHM, no equation relates the velocity and amplitude/period, nor is there anyway to find height.

Where in its swing does the pendulum have its maximum speed? And don't you have an equation that relates the amplitude to the maximum speed of a simple harmonic oscillator?
 
  • #9
Mister T said:
Well, realistically, yes. But if you want to be realistic the given period wouldn't be correct, would it?
That's my point, the period is not helpful. It should be much more reliably calculated from the amplitude via energy. That said, we do not really know the pendulum length - the mass centre will be higher than the seat.
So, yes, it would be worth going the amplitude and period route, at least to see how different the answer is.
dantechiesa said:
All we have learned in SHM, no equation relates the velocity and amplitude/period
So what equations do you have for SHM? You did not quote any in the template.
 

FAQ: What a I doing wrong? Swing/pendulum Questioj

1. Why is my swing/pendulum not swinging smoothly?

There could be several reasons for this. It could be due to an uneven or unsteady surface, incorrect weight distribution, or incorrect positioning of the pivot point. It could also be caused by air resistance or friction. Try adjusting these factors to see if it improves the swinging motion.

2. How do I determine the correct length for my pendulum?

The length of a pendulum affects its period, or the time it takes for one full swing. The longer the pendulum, the longer the period. To determine the correct length, you can use the formula T = 2π√(L/g), where T is the period, L is the length of the pendulum, and g is the acceleration due to gravity. Make sure to use consistent units for accuracy.

3. Why does my swing/pendulum eventually come to a stop?

The swing or pendulum comes to a stop due to the dissipation of energy through various forms of friction. This includes air resistance, friction at the pivot point, and internal friction within the materials of the swing. To minimize this, try using smoother materials and a lubricant at the pivot point.

4. Can I change the period of a pendulum by changing its mass?

No, the period of a pendulum is not affected by its mass. It is only affected by the length of the pendulum and the acceleration due to gravity. This is known as the "isochronous property" of pendulums, which means that all pendulums with the same length will have the same period, regardless of their mass.

5. What is the difference between a simple pendulum and a physical pendulum?

A simple pendulum is a point mass attached to a weightless and frictionless string, while a physical pendulum has a physical shape and mass distribution. The motion of a simple pendulum can be described by a single variable, the angle of displacement, while the motion of a physical pendulum is more complex and requires multiple variables to describe.

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