Something to think about on the treadmill

Kinetic energy relative to what?

I would say, relative to the floor, the runner is in fact at rest and therefore has no kinetic
energy (other than the small amount he has when he drops down to the floor).

Relative to the spinning treadmill, he does have kinetic energy. If he turned around backwards, he
would discover it very quickly.

Scott (NOT a member of the math or physics departments here! 🙂

Terry R. McConnell said:

First, some physics:

Moving bodies have a form of energy called kinetic energy that is proportional to the product of
mass and the square of velocity. Because of the square, kinetic energy grows very quickly with
increasing velocity. A speeding rifle bullet carries enough kinetic energy to knock a large person
to the ground even though it may weigh only a few grams.

Like any other moving body, runners acquire kinetic energy when they begin their run.
(Technically, they already had the energy in another form: stored chemical energy.) This energy
of motion can also be considerable: run into an immovable object and that energy will be quickly
and painfully dissipated, some in the form of heat, the rest in the form of sound energy. (A
loud SPLAT.)

Now imagine that same runner on a treadmill. He/she has used just as much chemical energy to
accelerate to running speed relative to the belt as a runner on the road. But what if the
treadmill were suddenly jerked out from under the runner while in mid stride? What would happen?
Would they go flying? Or would they simply land on the floor, bewildered, but otherwise none the
worse for wear? If the latter, what happened to all their kinetic energy?

Terry R. McConnell said:

Quoted message said:

First, some physics:

Moving bodies have a form of energy called kinetic energy that is proportional to the product of
mass and the square of velocity. Because of the square, kinetic energy grows very quickly with
increasing velocity. A speeding rifle bullet carries enough kinetic energy to knock a large
person to the ground even though it may weigh only a few grams.

Terry - While the rest of your concept might be right, your contention that a bullet will knock a
person down is wrong. I have watched many tapes of Richard Davis (Creator of Second Chance Body
Armour) demonstrating his product by being shot point blank with high power rifles. it never even
knocks him off balance, much less knocks him down. Its not the bullet that knocks a person down, its
the damage it does to the body (broken bones, severed arteries, ruptured organs, etc.). Ask a hunter
sometime about whether or not a bullet actually knocks a deer down or not. What you see on TV and in
the movies NEVER happens. People are not knocked off their feet. In fact many times they never
realize they have been hit until the damage caused by the bullet causes them to simply fall down.

Quoted message said:

Quoted message said:

Now imagine that same runner on a treadmill. He/she has used just

as

Quoted message said:

Quoted message said:

much chemical energy to accelerate to running speed relative to the belt as a runner on the road.
But what if the treadmill were suddenly jerked out from under the runner while in mid stride?
What would happen? Would they go flying? Or would they simply land on

the

Quoted message said:

Quoted message said:

floor, bewildered, but otherwise none the worse for wear? If the latter, what happened to all
their kinetic energy?

I run on a treadmill all the time. It has stopped suddenly, without warning on several occassions. I
did not go flying, and since trhere is no forward motion, I simply stopped, albeit quite suddenly
and with a desire to keep going. In this case, I suspect that the lack of motion/momentum is the
determining factor. I have been jogging thru the airport (or some of the local casino's) and was
using the moving sidewalk to speed things up when I either sudedenly reached the end of the
sidewalk, or had it stop without warning. in those cases, my forward momentum kept me moving,
sometimes causing a loss of balance.

Bruce

In article said:

First, some physics:

Moving bodies have a form of energy called kinetic energy that is proportional to the product of
mass and the square of velocity. Because of the square, kinetic energy grows very quickly with
increasing velocity. A speeding rifle bullet carries enough kinetic energy to knock a large person
to the ground even though it may weigh only a few grams.

Like any other moving body, runners acquire kinetic energy when they begin their run.
(Technically, they already had the energy in another form: stored chemical energy.) This energy
of motion can also be considerable: run into an immovable object and that energy will be quickly
and painfully dissipated, some in the form of heat, the rest in the form of sound energy. (A
loud SPLAT.)

Now imagine that same runner on a treadmill. He/she has used just as much chemical energy to
accelerate to running speed relative to the belt as a runner on the road.

That doesn't mean that kinetic energy is acquired.

Quoted message said:

But what if the treadmill were suddenly jerked out from under the runner while in mid stride? What
would happen? Would they go flying?

No. You'd have a very hard time balancing though, because you are moving in anticipation of the belt
moving rapidly underneath you. So when it doesn't, it's a really rude shock and you stumble. But you
don't go flying through the air.

Quoted message said:

Or would they simply land on the floor, bewildered, but otherwise none the worse for wear? If the
latter, what happened to all their kinetic energy?

When you hit the ground, that's where the energy goes (and heat). However, if the object you collide
into is "grounded", your energy is dissipated over a large area/mass, so the earth will only shake
if there is an enormous impact force.

Cheers,
--
Donovan Rebbechi pegasus.rutgers.edu~elflordOpen ↗

Terry R. McConnell said:

what happened to all their kinetic energy?

It's been sucked up into the electric motor that's turning the belt, and further into the electric
utility grid that powers the motor. All that stuff gets hot - that's where the energy goes.

Wakeley Purple said:

Terry R. McConnell said:

what happened to all their kinetic energy?

On a motorized treadmill, you're putting no energy into moving the treadmill at all. Imagine
if your treadmill was turned off. You'd have to exert force to get the belt to move, to
overcome its inertia and friction. The belt would exert an equal and opposite force back at
you, so you'd fly forwards off the treadmill and it would spin. On a motorized treadmill,
you are not pushing against the treadmill. You know this because you can run on it without
flying forwards, even if you don't hold onto anything. No force means no energy, nothing
transferred to the treadmill's spin. Most of your body mass is not moving relative to the
room. You are merely moving your legs to keep your feet in contact with the belt. Your
energy goes into various parts of your body in ways I don't quite understand. It has
something to do with inelasticity in your body, shoes, and the belt. If your body were
perfectly elastic, you'd only have to take one stride and your legs would continue to bounce
back and forth like pendulums. Also, you are spending energy on those little "hops" up and
down. Again, if you were perfectly elastic, you'd bounce like a rubber ball with just one
step, and no effort. You could run for miles without fatigue! You can see why your coaches
tell you to bounce as little as possible, and why shoe companies try to market springy
shoes. Instead, the inelasticity dissipates most of your kinetic energy into heat. A little
energy also goes into wear and tear on the treadmill, your shoes, and your body. There are
other ways to lose energy - wind resistance on your legs, for example, but that is a whole
other can of worms. Note that *most* of the chemical energy in your muscles doesn't go into
movement in the first place. It is "wasted" as heat, which is why you have to sweat so much
when you run.

[DISCLAIMER] I am not a Physicist. If I were an actually physicist, I would have better things to do
than answer hypothetcial questions. (well, maybe not)

In article said:

Terry R. McConnell said:

what happened to all their kinetic energy?

It's been sucked up into the electric motor that's turning the belt, and further into the electric
utility grid that powers the motor. All that stuff gets hot - that's where the energy goes.

Very good, you win the prize.

One poster spoke of kinetic energy "relative" to the belt. Energy is not a relative quantity.
(Technically, it is a scalar, not a vector.) Momentum is a vector, at least in nonrelativistic
mechanics, so the poster may have been confusing kinetic energy with momentum.

Donovan claimed that the treadmill runner's kinetic energy was liberated when he hit the floor after
the treadmill had been yanked from under him, in part in the form of acoustic energy. (Did anyone
hear that yelp of surprise?) That would only account for the small increment in gravitational
potential energy the runner acquired when he first climbed aboard the machine.

To expand a bit on this poster's explanation, in a treadmill motor running under no load there will
be a small but nonzero phase angle (dwell angle) between the current in the armature and the current
in the rotor. The energy cost of this angle can be described by a suitable potential function. When
the runner climbs on and accelerates up to speed, the motor is running under increasing load, and
the energy expended by the runner is stored in a changed value of the dwell angle. When the
treadmill is abruptly moved, it notices the departure of its passenger as much (or more) than the
passenger himself. The stored energy is released as the phase angle reverts to its unloaded value.
In a nutshell: the energy goes with the treadmill.

Where that energy goes next is less clear. Some of it is probably dissipated on the rotor side: the
motor may rev a bit, and its housing might rattle. On the armature side, some of the energy
propagates back up the powerline in the form of back emf. Ultimately, water may issue just a bit
faster from the penstocks of the Robert Moses power dam. The ratio of these two effects would depend
on the efficiency of the motor.

--
************************************************************************
Terry R. McConnell Mathematics/215 Carnegie/Syracuse, N.Y. 13244-1150 [email hidden] 229B Physics
Bldg barnyard.syr.edu~tmcOpen ↗
************************************************************************

"Terry R. McConnell" <[email hidden]> wrote in message "]news:[email hidden]...

Quoted message said:

Very good, you win the prize.

One poster spoke of kinetic energy "relative" to the belt. Energy is not a relative quantity.
(Technically, it is a scalar, not a vector.)

Since velocity is a vector and kinetic energy is one-half * mass * velocity squared, then kinetic
energy is a vector.

--
Patrick

In article said:

"Terry R. McConnell" <[email hidden]> wrote in message "]news:[email hidden]...

Quoted message said:

Very good, you win the prize.

One poster spoke of kinetic energy "relative" to the belt. Energy is not a relative quantity.
(Technically, it is a scalar, not a vector.)

Since velocity is a vector and kinetic energy is one-half * mass * velocity squared, then kinetic
energy is a vector.

If you mix high school physics with grown-up physics, you can do some really interesting things,
especially if you add a dash of creativity to the mix.

What I'd like to know is, precisely how does one "square" a vector ?

Cheers,
--
Donovan Rebbechi pegasus.rutgers.edu~elflordOpen ↗

"Terry R. McConnell" <[email hidden]> wrote in message "]news:[email hidden]...

Quoted message said:

First, some physics:

Moving bodies have a form of energy called kinetic energy that is

proportional

Quoted message said:

to the product of mass and the square of velocity. Because of the square, kinetic energy grows
very quickly with increasing velocity.

<snip>

Quoted message said:

Now imagine that same runner on a treadmill. He/she has used just as much chemical energy to
accelerate to running speed relative to the belt as a runner on the road. But what if the
treadmill were suddenly jerked out

from

Quoted message said:

under the runner while in mid stride? What would happen? Would they go flying? Or would they
simply land on the floor, bewildered, but otherwise none the worse for wear? If the latter, what
happened to all their kinetic energy?

Moving bodies possess kinetic energy. A runner on a treadmill does not move most of their mass
much at all.

Patrick Aro said:

"Terry R. McConnell" <[email hidden]> wrote in message "]news:[email hidden]...

Quoted message said:

Very good, you win the prize.

One poster spoke of kinetic energy "relative" to the belt. Energy is not a relative quantity.
(Technically, it is a scalar, not a vector.)

Since velocity is a vector and kinetic energy is one-half * mass * velocity squared, then kinetic
energy is a vector.

--
Patrick

If you can tolerate a lay question, if kinetic energy is a function of velocity, don't you have 2
frames of reference for determining the velocity of the runner, namely, the belt or the floor?

It seems like a trick question, because Terry's switching the context for determining velocity, and
therefore the resultant kinetic energy.

Scott (wayyyyy over his head)

"Donovan Rebbechi" <[email hidden]> wrote in message "]news:[email hidden]...

Quoted message said:

In article <[email hidden]>, Patrick Aro

Quoted message said:

Quoted message said:

"Terry R. McConnell" <[email hidden]> wrote in message
"]news:[email hidden]...

Quoted message said:

Very good, you win the prize.

One poster spoke of kinetic energy "relative" to the belt. Energy is

not a

Quoted message said:

Quoted message said:

Quoted message said:

relative quantity. (Technically, it is a scalar, not a vector.)

Since velocity is a vector and kinetic energy is one-half * mass *

velocity

Quoted message said:

Quoted message said:

squared, then kinetic energy is a vector.

If you mix high school physics with grown-up physics, you can do some

really

Quoted message said:

interesting things, especially if you add a dash of creativity to the mix.

What I'd like to know is, precisely how does one "square" a vector ?

My mistake. Velocity squared is a dot product making both it and kinetic energy scalar. However,
that's high school physics. How does a grown-up define scalar and vector quantities?

--
Patrick

"DrLith" <[email hidden]> wrote in message

Quoted message said:

Moving bodies possess kinetic energy. A runner on a treadmill does not

move

Quoted message said:

most of their mass much at all.

... relative to the floor below the treadmill, that's true... but I think the runner is still moving
their mass in the same way they would if they were running outside.

Imagine you are on a big ocean liner that happens to be going your exact running pace as you jog
along the deck in the reverse direction. This is the same situation. Only the size of the
"treadmill" changed.

cheers,
--
David (in Hamilton, ON) www.allfalldown.org

SwStudio said:

"DrLith" <[email hidden]> wrote in message

Quoted message said:

Moving bodies possess kinetic energy. A runner on a treadmill does not

move

Quoted message said:

most of their mass much at all.

... relative to the floor below the treadmill, that's true... but I think the runner is still
moving their mass in the same way they would if they were running outside.

This is really stupid. How can you possibly be moving your mass when there is an electric motor
turning the belt under your feet? You are not moving your mass forward, you are just keeping up with
the belt, and therefore using much less energy.

Quoted message said:

Imagine you are on a big ocean liner that happens to be going your exact running pace as you jog
along the deck in the reverse direction. This is the same situation. Only the size of the
"treadmill" changed.

Serious question: Are you really this stupid? The deck and your feet are all that count, not if the
ship is moving or not.

Quoted message said:

The stored energy is released as the phase angle reverts to its unloaded value. In a nutshell: the
energy goes with the treadmill.

I don't think that the treadmill generates energy. When the runner is removed the treadmill, it has
less of a load and therefore pulls less energy(current,power) from the wall.

Quoted message said:

Where that energy goes next is less clear. Some of it is probably dissipated on the rotor side:
the motor may rev a bit, and its housing might rattle. On the armature side, some of the energy
propagates back up the powerline in the form of back emf. Ultimately, water may issue just a bit
faster from the penstocks of the Robert Moses power dam. The ratio of these two effects would
depend on the efficiency of the motor.

It is a nice story but not how synchronous AC motors / Generators work.

Steve W.

"Bagpoop" <[email hidden].> wrote in message

Quoted message said:

SwStudio said:

Quoted message said:

"DrLith" <[email hidden]> wrote in message

Moving bodies possess kinetic energy. A runner on a treadmill does not move most of their mass
much at all.

... relative to the floor below the treadmill, that's true... but I think the runner is still
moving their mass in the same way they would if they were running outside.

This is really stupid. How can you possibly be moving your mass when there is an electric motor
turning the belt under your feet? You are not moving your mass forward, you are just keeping up
with the belt, and therefore using much less energy.

I don't think this is the way it works. It may seem that way, but in fact you are basically
expending the same amount of energy whether on a treadmill or outside (ignoring wind factors, etc.).

Quoted message said:

Quoted message said:

Imagine you are on a big ocean liner that happens to be going your exact running pace as you jog
along the deck in the reverse direction. This is the same situation. Only the size of the
"treadmill" changed.

Serious question: Are you really this stupid? The deck and your feet are all that count, not if
the ship is moving or not.

You misunderstood - I agree. I was making the point to illustrate why your above opinion about the
treadmill was an fallacy that many (including myself, previously) believed to be true. Replacing the
treadmill with the ship deck should, in theory, change nothing.

cheers,
--
David (in Hamilton, ON) www.allfalldown.org