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Old May 24th 2017, 12:23 AM   #1
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Pendulum impact force

Hi,

I'm trying to figure out the impact force of a pendulum at its max speed. My take on this is to use 2 equations:

Everything here is known except the velocity v

Potential/Kinetic energy
m*g*h=1/2*m*v^2
which for a pendulum can be written
v=sqrt(2*g*L*(1-cos(theta))

Impact force
F=m*Delta V/Delta t

And from this I can find the impact force?

My concern is that the mass is not a consideration for calculating the velocity.

Last edited by cpoulsen2; May 24th 2017 at 12:25 AM.
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Old May 24th 2017, 11:41 AM   #2
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The fact that mass doesn't enter into the velocity equation doesn't matter. You can calculate the velocity of the pendulum from the first equation, and then you can calculate the force it imparts if it hits something from the second, but you will have to assume (a) the final velocity after impact and (b) the duration of the impact event - in other words Delta t.
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Old May 24th 2017, 05:36 PM   #3
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Yes that was my way too. My assumption will be the impact is 0.1 s, which I think it's fair.

I just have a hard time getting my mind around it practically. I can't understand that not putting more weight on the end of the pendulum will not increase the velocity. From the equating it's clear, but practically, it's not.

Are there any other way I can calculate the impact? Without taking the time into consideration?
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Old May 24th 2017, 06:58 PM   #4
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Putting more mass on the pendulum doesn't increase its velocity for the same reason that a heavy mass doesn't fall faster than a light mass (as Galileo famously showed). But increasing m does increase the impact force calculation, since F =m delta_v/delta_t.
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Old May 25th 2017, 08:11 AM   #5
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So will it be a correct assumption that the potential energy = Force provided by the pendulum? Since the potential energy will be the same for a pendulum and free fall?
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Old May 25th 2017, 08:26 AM   #6
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Potential energyy has units of energy (joules), whereas force hasunits of newtons, so no - they are not equal. Since the impact force is proportional to mass times velocity, and velocith is proportipnal to the square root of the starting height of the pendulum, you can say that the impact force is proportional to mass times ther square root of h (assuming delta t is not affected by velocity).
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