# Expression for work done

1. Jul 28, 2011

### Alpharup

I have studied in my lower grades that work(w) done or energy is the product of force(f) and displacement(s).Till now I was thinking that this was true. I was not taught that it was the dot product of force and displacement. according to this definition, the work done when the force and displacement are mutually perpendicular to each other is zero. Now my question is whether this expression is based on real life experiences or was it designed to give only the dot product?

2. Jul 28, 2011

### Studiot

Hello sharan,

Since you have reached the dot product, you must have encountered a wide variety of physics by now.

So you might like to ask yourself

What sort of 'force' is there that can cause a displacement at right angles to its line of action?

3. Jul 28, 2011

### Alpharup

Yes I do ask. I conducted a small experiment. I placed two pencils at right angles to each other. The pencils were not in contact and they were kept a few centimeters apart. I measured the diameter of the pencils and kept them in such a way that when I pushed one of the pencil it touched the other at the end. After keeping a few distance apart I pushed one of the pencils towards the other in such a way that it hit the other pencil's end perpendicularly. There was little displacement in the other pencil which was at rest perpendicular to the force of pencil in motion. Here displacment was possible due to the work done. So the pencil which had a certain force caused displacement in the other pencil. So explain me now how work done satisfies dot product? If dot product was to be real the work done must be zero. Then how would it have caused displacement?

4. Jul 28, 2011

### rcgldr

That type of collision will result in both linear and angular reactions. The linear reaction is a function of the force times distance, regardless if the pencil is hit at the end or at the middle. The difference is that the struck pencils linear inertia is less if struck at the end instead of the middle, so the force involved is less.

If a force is always oriented so it's perpendicular to the path of an object, the speed will remain constant and only the direction will change. One common example of this would be steering a car to make it turn.