- #1
MalachiK
- 137
- 4
I've always thought of work done as being calculated by something like ∫F.dx whenever a force acts on a moving body. Another way of writing this ∫F.vdt. The non integral form of this equation (W = Fv) makes sense to me in the situation where the body is moving at a constant velocity as the driving force is doing work against some constant frictional force or whatever.
But in the case where F is the only force acting (or where F is the resultant force) and the velocity of the body is changing then it would seem that the force does different amounts of work in different directions.
Let's say that there's a body moving though space at a few km/s in some direction. If I apply a force in the direction of the velocity then it will do some work accelerating the body = ∫F.vdt. While this force acts the object moves though a large distance and so the work done is large.
Whereas, if the same magnitude force acts perpendicular to the velocity for the same amount of time then the displacement in the direction of the force is small and therefore little work is done. Let's say that these forces are produced by burning fuel. To produce the same force for the same duration must require the same quantity of fuel. So if one force does more work, where does the energy go?
I know that forces can act without doing work (e.g. supporting a weight against gravity) and that kinetic energy scales with v2, making small changes in the speed have a large effect on the kinetic energy when things are moving quickly. But it doesn't seem to make sense that burning the same amount of fuel to produce the same magnitude translational accelerating forces for the same durations should result in different amounts of work being done.
Clearly something is wrong with my understanding! Could somebody make some suggestions on how I could clear this up?
Thanks
But in the case where F is the only force acting (or where F is the resultant force) and the velocity of the body is changing then it would seem that the force does different amounts of work in different directions.
Let's say that there's a body moving though space at a few km/s in some direction. If I apply a force in the direction of the velocity then it will do some work accelerating the body = ∫F.vdt. While this force acts the object moves though a large distance and so the work done is large.
Whereas, if the same magnitude force acts perpendicular to the velocity for the same amount of time then the displacement in the direction of the force is small and therefore little work is done. Let's say that these forces are produced by burning fuel. To produce the same force for the same duration must require the same quantity of fuel. So if one force does more work, where does the energy go?
I know that forces can act without doing work (e.g. supporting a weight against gravity) and that kinetic energy scales with v2, making small changes in the speed have a large effect on the kinetic energy when things are moving quickly. But it doesn't seem to make sense that burning the same amount of fuel to produce the same magnitude translational accelerating forces for the same durations should result in different amounts of work being done.
Clearly something is wrong with my understanding! Could somebody make some suggestions on how I could clear this up?
Thanks