Understanding the Concept of Work: Displacement of Force or Center of Mass?

[Rusag]

I am having trouble understanding the concept of work on an intuitive level. The equation is rather simple but the definition of displacement is vague (everywhere I looked it's just stated as displacement of the body in the direction of motion). The question is, is this the displacement of the point of the application of a force or the displacement of the center of mass of the body?

 

[rootone]

Displacement is simply the distance moved.
Let's say the object is simple ball, we can measure that distance in a number of ways.
Measuring the distance in terms of the distance traveled by it's center gravity would be one obvious way,
but you could measure the distance which the surface of the ball has traveled and will still get the same number.
(we don't need to take into account ideas such as that the ball might be rotating while it moves, only the distance moved overall along some known vector)

 

[jbstemp]

The displacement of the center of mass of an object should be the same as the displacement of any other point, assuming the object is rigid (doesn't stretch or contract).

 

[Apogee]

Assuming an object moves a distance x, every point on the object moves that distance unless the object deforms. Therefore, measuring work of any point on the object should be the same. It's actually a pretty interesting idea when you think about it. :)

 

[jbriggs444]

It is the displacement of the target object at the point of application of the force. If you compute work done based on the motion of the center of mass of the body then you would be computing "pseudo-work" or "center of mass work". If you want true work (and assuming that the object is either rotating or is non-rigid) then you need to look at the motion of the point on the target where the force is applied.

 

[Rusag]

Thank you all for the replies! It's starting to make sense now. The question that made me think about this involved a rod attached at one end and a force acting at the other end. In other words, both the center of mass and the endpoint of the rod trace a circular path, however due to the radii difference from the fixed end to those two points the end moves further, hence the work is greater in this case. To sum it all up, we have to look at the displacement of the point of application of a force, if the object is rotating, yet if the object is simply moving it would be enough to know the displacement of its center of mass?

 

[jbriggs444]

To sum it all up, we have to look at the displacement of the point of application of a force, if the object is rotating, yet if the object is simply moving it would be enough to know the displacement of its center of mass?

Yes. For rigid objects that summary is correct.