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A table holding a book up is exerting force on the floor. That is not work.
Irrelevant.FactChecker said:A table holding a book up is exerting force on the floor. That is not work.
In a frame where the floor moves downwards, the table is doing work on it.FactChecker said:A table holding a book up is exerting force on the floor. That is not work.
If the treadmill is inclined they all do work on the belt, in the frame of the gym.FactChecker said:Force times distance at the point of contact. At the point of contact with the treadmill, here is no difference in force between: 1) a person walking on the treadmill, 2) a person standing on the treadmill, and 3) a lead block of the person's weight sitting on the treadmill.
FactChecker said:A person on a treadmill is not changing the motion of the treadmill. The treadmill surface would be moving the same way if no one was on it.
Comparing different joint positions is irrelevant for walking on the treadmill vs. ground, which both can be achieved with the same joint kinematics.FactChecker said:If we try to make a consistent definition of work that will distinguish between a person hanging from a bar with his arms extended versus a person hanging from a bar in a "pull up" position, we will fail.
Given a runner on a moving treadmill belt, viewed from a frame of reference in which the exercise room is at rest, the dot product of the force of shoes on belt times distance moved by belt under those shoes is non-zero.FactChecker said:Force times distance at the point of contact.
FactChecker said:walking on an inclined treadmill is work.
You're applying a force to the treadmill.FactChecker said:Not true. Gravity is the only force being opposed.
Yes he is. Imagine the treadmill could free-spin or imagine it was ice. If you tried to run on it you'd fall on your face and slide off the back. The treadmill must apply a force forward to hold you up against gravity.This is not similar to a hovering helicopter because the helicopter is pushing the air around and a person on an inclined treadmill is not pushing the treadmill down.
You are letting that confuse you: the fact that the treadmill moves on its own doesn't tell you anything about the forces on it.The treadmill surface is rotating down on its own and would do that if no one was on it. I have not "glossed over" the problem.
We're discussing the standard definition, you're just applying it to the wrong thing.I have thought about this several times over decades and could not come up with a consistent definition of "work" other than the standard one.
I stand corrected. I could not accept that a block of lead being lowered on a treadmill was doing work. I guess I was not correctly applying the definition of work.A.T. said:If the treadmill is inclined they all do work on the belt, in the frame of the gym.
For what it's worth, that block of lead can be seen as exerting two forces: a contact force on the treadmill belt and a gravitational force on the Earth. The contact force is doing positive work -- it is a downward force on a downward moving belt. The gravitational force is zero work -- it is an upward force on a motionless Earth.FactChecker said:I stand corrected. I could not accept that a block of lead being lowered on a treadmill was doing work. I guess I was not correctly applying the definition of work.
phinds said:jbriggs, I usually find your comments spot on but I think you seriously missed the boat on this one. (1) The treadmill moves exactly the same whether you are on it or not and (2) yes it DOES matter that you are not raising your center of mass.
At this point, I think that we are all on the same page and are preaching to the choir.lesaid said:Can one not simplify the thought process by imagining a sealed corridor with no windows - set on the side of a hill, and someone walking up it. He will do a certain amount of work to get from the bottom to the top of the corridor.
Yeah, I think that's where my head was. The runner's center of mass didn't move upward on the treadmill so I looked no further. Thank you for your extensive and lucid discussion in this thread.jbriggs444 said:My suspicion is that a meta-problem was confirmation bias. With an experimentally confirmed effect in hand and a semi-plausible explanation, one is not going to be very receptive to someone saying that it's all wrong.
jbriggs444 said:At this point, I think that we are all on the same page and are preaching to the choir.
The motor absorbs work in preventing the belt from slipping.Grinkle said:Agreed.
Moving the discussion what is the simplest way to look at it, I claim that the work being done is most easily calculated by looking at the torque vs radial displacement of the treadmill motor. This motor is moving the runners center of mass down the belt as the runner moves themself back up the belt. The motor does work in preventing the belt from slipping.
The motor's work must be the additive inverse of the runner's work [ignoring frictional losses].Neglecting heat dissipation in the friction of the treadmill (not trivial for most treadmills I suppose), the motor work must be the runners work.
What is "apparent gain in height", and why is it relevant?rude man said:We both say the apparent gain in height on a treadmill is far greater than that of climbing an actual mountain.
The crucial parameter would the speed of the belt. If there is only negligible variation of belt speed, you can define an inertial frame where the support surface is at rest. Per Galilean Invariance this frame is equivalent to the rest frame of a hill incline (ignoring air drag). So there is no physical reason to walk differently and do different work, just psychological ones.Roger Chase said:The Yellow waveform is the brushed DC motor current, Blue (which is kind of obscured in the background) is the PWM'ed motor voltage and the Red is their product (power in Watts).View attachment 212748
Yes, of course. The equivalence is to a smooth constant slope hill.lesaid said:I know personally, it takes substantially more effort to hike up a rough, uneven slope than a smooth steady gradient, and found a treadmill easier.
That can make it completely different, depending on how much force you put on the rails.lesaid said:When on a treadmill, there is also the temptation to rest one's hands on the rail - while serious users presumably may not do this - doing that could help a lot with maintaining balance, increasing the efficiency of the walking/running?
What argument that what is half the effort of what?Sherwood Botsford said:This would support the argument above that it's about half the effort.
You are going to have to make this argument more detailed. As it stands, it is not even wrong.votingmachine said:When you walk up a real hill, you never get the "ride".
During the downstroke on a moving treadmill, your muscles are contracting and your leg is extending. The "just rides down" verbiage suggests that you believe that no effort is expended and no work is being done.You do lift your foot to move it up the treadmill. But then it just rides down
The word obvious is the clue that this is the error.It seems obvious that there was less work
votingmachine said:Moving two feet can seem to be that same motion.
Each time you are carried back and down, you lose potential energy, which ends up in the motor-drive assembly - either as a reduction in energy supplied to the motor, or as in heat from a brake, perhaps.Sherwood Botsford said:I stand on the belt, and move backward dropping 10 cm.
I then take two steps forward rising 10 cm.