Stop a Pendulum: Calculate Stopping Force

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Discussion Overview

The discussion revolves around calculating the stopping force for a pendulum, addressing two main problems: determining the force exerted when stopping the pendulum and calculating the energy lost after an impact. The scope includes theoretical considerations and practical implications related to pendulum motion and collisions.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant seeks a non-experimental method to calculate the stopping force of a pendulum when opposing its motion or placing an obstacle in its path.
  • Another participant suggests that the stopping force is dependent on the time interval over which the pendulum is stopped, indicating that an instantaneous stop would require an infinite force.
  • A different viewpoint states that if the pendulum is stopped at the bottom of its swing, the impulse required to stop it can be calculated using the mass and velocity of the pendulum, with energy lost equating to half the mass times the velocity squared.
  • Concerns are raised about the complexities of stopping a pendulum with a non-spherical mass and the variability of energy loss upon impact due to differing elasticities.
  • A participant questions the assumption that the force is theoretically zero at the highest point of the swing after impact, suggesting that there would still be a force applied when the pendulum begins to swing back.
  • Another participant expresses curiosity about the formula used in an applet for calculating tangential force, noting discrepancies in expected values at larger angles.

Areas of Agreement / Disagreement

Participants express differing views on the nature of forces acting on the pendulum at various points in its motion, particularly regarding the stopping force and energy loss upon impact. No consensus is reached on the exact calculations or methods to be used.

Contextual Notes

Limitations include the dependence on the specific conditions of the pendulum's mass and shape, the assumptions made about elasticity during impacts, and the unresolved nature of the mathematical steps involved in calculating forces and energy loss.

Who May Find This Useful

This discussion may be of interest to those studying dynamics, mechanics, or anyone involved in practical applications of pendulum motion and collisions.

samodelov.1
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I am looking for a way to calculate the stopping force for a pendulum but have two problems here. Number one is that I can not find any information on a (non-experimental) way of calculating the force a pendulum would have if you pulled against its direction of motion or put something in front of it. Second: I need to stop it after an initial impact and was wondering if anyone knows of a way to calculate the energy lost to a pendulum after impact. Thanks! Any and all help is appreciated!
 
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samodelov.1 said:
I am looking for a way to calculate the stopping force for a pendulum but have two problems here. Number one is that I can not find any information on a (non-experimental) way of calculating the force a pendulum would have if you pulled against its direction of motion or put something in front of it. Second: I need to stop it after an initial impact and was wondering if anyone knows of a way to calculate the energy lost to a pendulum after impact. Thanks! Any and all help is appreciated!

The stopping force depends directly on time interval within which you wand to stop it:
F=-dp/dt. Here dp is the current momentum minus the final momentum (=0 for stopped body), dt is the time interval during which you stop the body. For example, if you want to stop it instantly, the force should be inifinite.
If dt is much smaller than the oscillation period (dt<<T), you can speak of a constant force F=-dp/dt. If not, your force will time dependent as F(t)=-dp(t)/dt (ordinary derivative). Anyway, you have to spend the work=the body kinetic energy. At the turning point not force is necessary.

Bob.
 
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If you stop a pendulum at the bottom of its cycle, so that all of its energy is kinetic energy of the (point) mass itself, then the equations are the same as for a mass sliding horizontally without friction. In short, if the mass M has a velocity v, then the impulse to stop it is the integral of force F(t) times time dt = M v. The energy lost is just (1/2) M v2.

If the mass hits a rigid (infinite mass) stop and bounces off the stop with 100% coefficient of restitution, the direction of pendulum moton is changed, no momentum is transferred to the stop (because the integral F(x,t) dx is zero), and the pendulum loses no kinetic energy. In this case, the integral F(x,t) dt is doubled.

If the pendulum mass is finite size and therefore has angular momentum, then the mass has to hit the stop at the center of its percussion so that both the linear kinetic energy and the rotational kinetic energy are completely absorbed.

For a simple pendulum, you could put a mass equal to the pendulum mass at the bottom of the swing, and if the collision between the pendulum and the mass is completely elastic, all the momentum (and energy) would be transferred to the mass, and the pendulum would stop.
 
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Thanks for all the help! I think I am beginning to get a better picture of what is happening theoretically. (I was never good at circular motion.)

On a practical basis: My mass is not spherical, so it cannot impact at the center of percusion (or I can't ensure that it does, in any case) and it is impacting an elastic fixed body. I know now that there is no way of calculating exactly how much energy is lost at impact (the body changes and each has a different elasticity). I will just go with a worst case scenario and assume no energy is lost upon impact.

If I do try to stop the pendulum at it's highest point after it has impacted and changed direction, even though the force is theoretically zero, wouldn't there be a force applied to my stop once the pendulum begins to swing in the other direction again?

Thanks again!
 
samodelov.1 said:
If I do try to stop the pendulum at it's highest point after it has impacted and changed direction, even though the force is theoretically zero, wouldn't there be a force applied to my stop once the pendulum begins to swing in the other direction again?

Thanks again!

Why do you think the force is theoretically zero? Does it accelerate? Try drawing a graph of displacement/velocity/acceleration (use different colors) vs time. Or you can try this neat applet
http://www.walter-fendt.de/ph11e/pendulum.htm
 
Last edited by a moderator:
That applet is really helpful. Thanks!

What formula is it using to calculate the tangential force? I thought it was F=mg*sin(theta) but their maximum force always seems to be somewhat higher than that, especially at larger angles.
 

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