J
joshv
Guest
Kaz Kylheku wrote:
> Work is indeed force x distance, but those quantities are vectors and
> the x is a dot product. When you move against a resistance, you expend
> work. If the vectors are perpendicular (the movement is lateral with
> respect to that force) the dot product is zero. No work is done against
> that force.
>
> If you are running at constant elevation, the only net work you are
> doing is against air resistance and friction.
Actually, running is not purely horizontal. There is a lot of up and
down motion (in some people several inches each stride). This work is
entirely wasted, and it is directly proportion to the mass of the
individual. A quick back of the envelope calculation shows me that for
a 200 lbs runner, on a 5 mile run, a 4 inch bounce can waste 125
calories in purely vertical motion. This is why running mechanics are
so important. Don't bounce - glide
This is also why bicyclists prefer light bikes, and jockeys are so
tiny.
> You aren't doing any work
> due to your mass, against gravity. Extra body weight does not add to
> the work of actually moving from point A to point B, because that work
> is zero! The two vectors are perpendicular. Gravity points downward,
> and you are moving horizontally. The dot product is zero.
The force you are working against is mostly friction if there is no
wind. Friction is not perpendicular to the direction of motion, it is
parallel, directed opposite the direction of travel. Friction =
coefficient of friction * mass * g.
Want to prove it to yourself? Push a book across your desk. Note the
effort required. Now have a friend lean his weight on the book. Now
try to push it again. It will require more force to move it.
Similarly with human bodies in contact with the ground.
> In other words, it takes no energy to move a mass at constant speed in
> a straight line, when there is no external force that has any component
> in the direction of motion. It does take work to accelerate that mass
> to its cruising speed, and that work is later wasted when you use
> friction to brake that mass to a halt. Maintaining cruising speed is
> all about friction.
Exactly, and friction provides a force parallel to the direction of
travel. Friction is also directly proportional to mass. Thus the force
required to balance friction is directly proportional to mass.
> Work is indeed force x distance, but those quantities are vectors and
> the x is a dot product. When you move against a resistance, you expend
> work. If the vectors are perpendicular (the movement is lateral with
> respect to that force) the dot product is zero. No work is done against
> that force.
>
> If you are running at constant elevation, the only net work you are
> doing is against air resistance and friction.
Actually, running is not purely horizontal. There is a lot of up and
down motion (in some people several inches each stride). This work is
entirely wasted, and it is directly proportion to the mass of the
individual. A quick back of the envelope calculation shows me that for
a 200 lbs runner, on a 5 mile run, a 4 inch bounce can waste 125
calories in purely vertical motion. This is why running mechanics are
so important. Don't bounce - glide
This is also why bicyclists prefer light bikes, and jockeys are so
tiny.
> You aren't doing any work
> due to your mass, against gravity. Extra body weight does not add to
> the work of actually moving from point A to point B, because that work
> is zero! The two vectors are perpendicular. Gravity points downward,
> and you are moving horizontally. The dot product is zero.
The force you are working against is mostly friction if there is no
wind. Friction is not perpendicular to the direction of motion, it is
parallel, directed opposite the direction of travel. Friction =
coefficient of friction * mass * g.
Want to prove it to yourself? Push a book across your desk. Note the
effort required. Now have a friend lean his weight on the book. Now
try to push it again. It will require more force to move it.
Similarly with human bodies in contact with the ground.
> In other words, it takes no energy to move a mass at constant speed in
> a straight line, when there is no external force that has any component
> in the direction of motion. It does take work to accelerate that mass
> to its cruising speed, and that work is later wasted when you use
> friction to brake that mass to a halt. Maintaining cruising speed is
> all about friction.
Exactly, and friction provides a force parallel to the direction of
travel. Friction is also directly proportional to mass. Thus the force
required to balance friction is directly proportional to mass.