Speed as a ratio, but what about work done and moments?

[rvgene]

Hi all,

Speed is a ratio of the distance traveled per unit time. But what then is work done and moments?

For example, work done is force multiplied by the distance traveled in the direction of the force. But how would you explain the rationale of multiplying these two quantities?

As in, in the case of speed, the unit is m/s, which makes sense, but something like moments, with units of Nm, it looks as though it does not make much sense.

 

[russ_watters]

Welcome to PF!

There is no mystery here. These are all just useful mathematical relationships people figured out once upon a time. There's nothing special about multiplying or dividing...or squaring, for that matter... to get them.

However: Speed is a rate. An amount of something done per unit time. Any measure of an amount of something done per unit time is divided by time. Whether it's power (J/s), rotational rate (r/m or rpm), or hot dogs eaten per hour on dollar dog day (Hotdogs/h).

 

[rvgene]

I am just wondering why work done is force x distance and not, let's say force/distance.

How did the idea of work done being force multiplied by distance come in the first place?

 

[I like Serena]

I am just wondering why work done is force x distance and not, let's say force/distance.

How did the idea of work done being force multiplied by distance come in the first place?

If you move an object over twice the distance, it's twice as much work.

 

[rvgene]

If you move an object over twice the distance, it's twice as much work.

ahh... that makes more sense now. same thing for moments right?

 

[I like Serena]

ahh... that makes more sense now. same thing for moments right?

Yep!

Most of these equations (can) come about by thinking about them and considering whether the relationship will be linear or inversely linear.

Thinking about it that way will also give you an intuitive understanding that IMO is very important!