Work, then Force, then Acceleration

[bravoghost]

So I started connecting some dots, and got lost. Work=Force x Distance. Of course. Force = mass x acceleration. Of course. Acceleration must be non-zero in order for there to be a force present.

 

So imagine you're moving a box across the floor. You get the box moving, and from that point on you move at a constant velocity. The constant velocity indicates there is 0 acceleration, if there is 0 acceleration then 0 force is being applied. But that would mean that there is no work being done. But there must be work being done since the box is moving over a distance. How am I tripping up?

[DJBruce]

So I started connecting some dots, and got lost. Work=Force x Distance. Of course. Force = mass x acceleration. Of course. Acceleration must be non-zero in order for there to be a force present.

 

Work is [math] W=F\cdot d[/math] not [math]W=F X d[/math], and force is [math]F=ma[/math]. Neither of those have a cross product in them.

 

Velocity is the change in displacement with respect to the change in time. This means if you an object has velocity then it most be moving or changing directions. Work on the other hand is the idea that you are applying a force through a distance parallel. This does not mean that just because an object is moving some distance that it must be having work preformed on it.

Edited August 26, 2010 by DJBruce

[TonyMcC]

You had to do some work to get it moving. Momentum will keep it moving. Some work is needed to slow it down or bring it to rest. In practice work is needed to maintain velocity due to resistance caused by friction etc..

[swansont]

Work is [math] W=F\cdot d[/math] not [math]W=F X d[/math], and force is [math]F=ma[/math]. Neither of those have a cross product in them.

 

 

I believe bravoghost was merely referring to scalar multiplication, rather than any vector products.

 

 

In any event, friction is a confounding factor in visualizing this; it is a reason that the Greeks thought that the natural state of motion was to be at rest. Newton changed this. The natural state of motion is constant velocity (all inertial frames are physically equivalent; i.e. there is no preferred frame) A box sliding on a frictionless surface will slide forever, ideally — nothing needs to be done to maintain this motion. You would have to exert a force and do work to stop it, as TonyMcC has noted, and the concept behind this is Newton's first law.

[bravoghost]

I suddenly realized the friction thing after the first post in this thread. It was a 'Eureka!' moment.

[lemur]

I find it interesting and perhaps ironic that an object in frictionless motion does not perform work, yet it does traverse distance. In a sense the object is both "in motion" and "at rest" at the same time. This confounds fixed-coordinate spatial thinking, but it also suggests some reason to the fact that light can transmit power across a distance without performing work to do so; at least it does imo.

Edited September 8, 2010 by lemur