Does Force Applied to Rigid Body Produce Equal Effect?

[batballbat]

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?

 

[JHamm]

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?

 

[batballbat]

i think the answer was affirmative. But take a lever for example. It ought to be not true.

 

[JHamm]

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.

 

[batballbat]

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.

 

[Doc Al]

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.

 

[batballbat]

think about billiard balls. i am sure there is a difference in acceleration

 

[Doc Al]

think about billiard balls. i am sure there is a difference in acceleration

Think about Newton's 2nd law.