Does Force Applied to Rigid Body Produce Equal Effect?

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Discussion Overview

The discussion centers on the effects of forces applied at different points on a rigid body, particularly regarding whether equal and parallel forces produce the same effects in terms of linear acceleration and torque. The scope includes theoretical considerations and mathematical reasoning related to mechanics.

Discussion Character

  • Debate/contested
  • Mathematical reasoning
  • Technical explanation

Main Points Raised

  • Some participants propose that a force applied at an arbitrary point on a rigid body can produce different effects depending on its point of application, particularly in terms of torque.
  • Others argue that two forces of equal magnitude and direction will produce the same acceleration in the center of mass, but question whether they could produce different torques.
  • A participant suggests that using a lever as an example demonstrates that the effects are not the same, as torque varies with the point of application.
  • Another participant emphasizes that in real-world scenarios, factors like friction complicate the situation, suggesting that the initial assumptions may not hold true.
  • One participant mentions billiard balls to illustrate that there may be differences in acceleration based on the point of force application.

Areas of Agreement / Disagreement

Participants express disagreement regarding the effects of forces applied at different points on a rigid body. While some agree that the center of mass acceleration remains constant with equal forces, others contend that torque and overall effects differ based on the application point.

Contextual Notes

Limitations include the dependence on definitions of force application points, the influence of external factors like friction, and the unresolved mathematical implications of torque calculations in specific scenarios.

batballbat
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a force is applied at a arbitrary point in a rigid body. Does another force equal to it and parallel to it applied to it another point produce the same effect?
 
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A force can produce an acceleration in the center of mass of a rigid body and a torque, two forces of equal magnitude and direction (parallel doesn't necessarily mean the same direction) will produce the same acceleration in the center of mass, do you think they could produce different torques?
 
i think the answer was affirmative. But take a lever for example. It ought to be not true.
 
Can you show it mathematically? Try a lever of length 1m, push with a force of 1N at the end and find that torque, then try again by pushing with 1N halfway along the rod.
 
i am sorry you misunderstood me. i was referring to JHamm quote
"Two forces of equal magnitude and direction (parallel doesn't necessarily mean the same direction) will produce the same acceleration in the center of mass"
In real word with friction this dosent seem true.
 
batballbat said:
a force is applied at a arbitrary point in a rigid body. Does another force equal to it and parallel to it applied to it another point produce the same effect?
As JHamm already explained:

If all you care about is the linear acceleration of the center of mass, then the point of application is irrelevant. The acceleration of the center of mass depends only on the net force, regardless of where the forces acting are applied.

But if you care about rotation as well as translation, then the point of application does make a difference.

So the short answer to your question is no. The same force applied at a different location will have a different effect.
 
think about billiard balls. i am sure there is a difference in acceleration
 
batballbat said:
think about billiard balls. i am sure there is a difference in acceleration
Think about Newton's 2nd law.
 

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