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

In summary: If you integrate the equation over time, you get a solution that gives the final velocity of the top of the pole.
  • #1
Charlie261
3
0

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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  • #2
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?
 
  • #3
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 verticle 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:
  • #4
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.
 
  • #5
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).
 

1. What factors affect the time it takes for a flag pole to fall over and hit the ground?

The main factors that affect the time it takes for a flag pole to fall over and hit the ground are the height of the flag pole, the weight of the flag pole, and the angle at which it falls. Other factors such as wind speed and surface conditions can also play a role.

2. Can the time it takes for a flag pole to fall over and hit the ground be predicted accurately?

It is difficult to predict the exact time it takes for a flag pole to fall over and hit the ground as it depends on various factors and variables. However, using mathematical equations and considering the factors mentioned above, it is possible to estimate the approximate time.

3. How does gravity affect the time it takes for a flag pole to fall over and hit the ground?

Gravity is the force that pulls objects towards the Earth. As the flag pole falls, it is pulled towards the ground by the force of gravity. The acceleration due to gravity (9.8 m/s²) affects the speed at which the flag pole falls, thus influencing the time it takes to hit the ground.

4. Does the material of the flag pole affect the time it takes to fall over and hit the ground?

The material of the flag pole can influence the time it takes to fall over and hit the ground. Lighter materials such as aluminum may fall faster than heavier materials such as steel. The shape and structure of the flag pole can also affect its speed and ultimately, the time it takes to hit the ground.

5. How can we measure the time it takes for a flag pole to fall over and hit the ground?

The time it takes for a flag pole to fall over and hit the ground can be measured using various methods such as using a stopwatch, video recording and analyzing the footage, or using sensors and data collection devices. The accuracy of the measurement will depend on the method used and the precision of the equipment.

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