What is the time taken for a flag pole to fall over and hit the ground?

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Homework Help Overview

The problem involves a 10m tall flag pole that topples over due to rust at its base. Participants are exploring the time it takes for the pole to hit the ground, considering the effects of gravity and the dynamics of the pole's fall.

Discussion Character

  • Mixed

Approaches and Questions Raised

  • Some participants attempt to apply kinematic equations to estimate the time of fall, while others question the assumptions of free fall, noting that the pole's toppling involves more complex dynamics.
  • Questions arise regarding the forces acting on the pole and the conditions necessary for it to fall, including the initial conditions that lead to its loss of balance.
  • There is discussion about the potential use of conservation of energy and angular motion to analyze the problem, with references to differential equations and elliptic integrals.

Discussion Status

The discussion is ongoing, with various interpretations and approaches being explored. Some participants express uncertainty about the existence of a straightforward solution, while others suggest more advanced methods that could be applied to understand the motion of the pole.

Contextual Notes

Participants note the complexity of the problem, indicating that it may not fit neatly into introductory physics frameworks. There is a mention of specific initial conditions that could affect the analysis, such as a small initial force to initiate the toppling.

Charlie261
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Homework Statement



The flag pole is 10m tall. The base of the pole has rusted and the pole topples over. What is the time taken for the pole to hit the ground?

s = distance = 10m
u = initial velocity = 0 m/s
v = final velocity = unknown
a = g = acceleration due to gravity = 9.81 m/s2
t = time taken



Homework Equations



s = ut + ½at2



The Attempt at a Solution



√2s/g = t = 1.43s

But this pole falling over is not in free fall. It is going to take longer. Please help.
 
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Charlie261 said:

Homework Statement



The flag pole is 10m tall. The base of the pole has rusted and the pole topples over. What is the time taken for the pole to hit the ground?

s = distance = 10m
u = initial velocity = 0 m/s
v = final velocity = unknown
a = g = acceleration due to gravity = 9.81 m/s2
t = time taken



Homework Equations



s = ut + ½at2



The Attempt at a Solution



√2s/g = t = 1.43s

But this pole falling over is not in free fall. It is going to take longer. Please help.

What is causing the pole to fall? What forces act on a perfectly vertical pole?
 
The base of the pole at ground level has completely rusted. One side of the pole at the base crumbles slightly just enough for the pole to not be vertical and so the pole is not balanced and the pole falls over due to gravity.

Another scenario would be that a person tried to balance a pole on its end. The pole is balanced and remains in the vertical for a few seconds and then loses balance and topples over. What would be the most time taken for a pole to move from the vertical to the horizontal due to the force of gravity alone?


Did not want to over complicate things but if it helps:

Assume a very small intial force at the top of the pole to make the pole not vertical.

ie. velocity of top of pole 1mm/s at a distance 1mm from the vertical position.

Assume there is no side ways movement at the base of the pole due to friction. ie rough ground.
 
Last edited:
Since nobody has come up with a solution I am beginning to think that there is no equation for an object falling over.
I was also hoping to work out the velocity that the top of the pole would hit the ground.

If someone could explain the difficulties of why there is no easy solution that would help me.
 
Charlie261 said:
Since nobody has come up with a solution I am beginning to think that there is no equation for an object falling over.
Oh, there are equations all right. You can use conservation of energy to determine how angular velocity depends upon the angle from vertical. Add in initial angular velocity to get the pole away from the vertical unstable equilibrium point and you end up with a differential equation to solve for angle versus time. I believe that this leads to some variety of elliptic integral to solve, which is not exactly "introductory material".
I was also hoping to work out the velocity that the top of the pole would hit the ground.
Well, that's an easy one. Conservation of energy (center of mass height change versus rotational velocity).
 

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