How far Should I Push It?

I am in the 4th grade, just starting to study physics. On a study sheet it says: ’If the effort increases, the distance decreases. If the effort decreases, the distance increases.’ My dad says this is backwards - can you help? Thank you.
- Robert Nusbaum (age 10)
Prospect, Oh, USA

It sounds like the study sheet that you mentioned is refering to the work needed to change an objects speed by a certain amount depends on the distance over which you the object is pushed. For instance, imagine you are pushing a sled on a sheet of flat, frictionless ice. If you push for a certain distance, then stop, then the sled will go sliding away at a constant speed until it hits something. If you want to push the sled up to the SAME SPEED as before, only now pushing it for a SHORTER distance, then the force you need to apply to the box (the effort) must be GREATER to get that sled moving as fast as before. The reverse is also true, that if you want to push with LESS force (less effort), then you will have to push the sled FARTHER to get it up to that same speed.

Your dad is correct that if you do MORE work on an object, then it will take a GREATER distance for friction to slow an object down. The question is what you define as "effort." In the case of your physics sheet, it seems that "effort = force" makes more sense than "effort = work." Force and work are not the same thing, though they are closely related. This is an important point. Force is a changing of momentum, while work is a measure of force applied over a distance. So in the end, work is not the amount of force, but how far you maintain that force.

dk

(published on 10/22/2007)