# Exercise: who does more work weight lifter/marathon runner

I was trying to identify which athlete does more work per rep/stride. I am trying to understand how a marathon runner can run sub 6 minute miles under aerobic conditions. To me this seems like a high intensity to I wanted to figure out who was doing more work, producing more force, or if you can think of a better measurement to compare the two.
My thoughts on how to calculate: w=f*d, f=m*a, p=w/t
Weightlifter performing dead lift: w=118kg * 9.8m/s/s*1 m = (correct) 1156.4 N

p=1156.4N/3s 386.467 W

I had some trouble with the runner because I was unsure of how to calculate w. would it be the runners weight (w in kg) * gravity * stride length, or would gravity have to be a component because they are not traveling say 6 feet straight up, but rather a matter of inches up and 6 feet in distance. stride length is about 1.17 times the height of the runner who is 6 feet, and lets say they elevate .15 meters. Lets also assume their stride takes .35s ( this is not unreasonable, I think I read 10k runners running at 180-190 strides per minute)

my experimental runner: 70kg, stride length 12.85 m, distance off the ground while running .15m, .35s per stride

If anyone has some input on how to solve the work of the runner I would appreciate it, or if you see some problems in my logic. (this is not homework, just fun work)

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Stephen Tashi
You'd have to consider physical work needed to breath.

Computing work, in the sense of force times distance isn't the whole story on energy expended since the body isn't 100% efficient as a machine. You can probably find data on the calories burned while doing various athletic activities, which would be a more direct measure of energy.

So, you are saying taking a marathon runners total calories burned then finding estimated burned per 3 seconds (assuming thats the amount of time a weight lifter takes to complete the deadlift) and comparing that to the weight lifters calories burned during their lift is a better measure?

Stephen Tashi
So, you are saying taking a marathon runners total calories burned then finding estimated burned per 3 seconds (assuming thats the amount of time a weight lifter takes to complete the deadlift) and comparing that to the weight lifters calories burned during their lift is a better measure?
Yes, calories used-up would be a better measure of actual energy expended that an analysis of mechanical force-times-distance.

The force-time-distance analysis is interesting. However, it is complicated. For example, in order to run, the mass of the legs must be moved in a complicated pattern. The leg is given acceleration in one direction and then this acceleration must be counteracted by giving it acceleration in another direction. That requires doing mechanical work. You can't get an accurate analysis just by looking at the motion of the runners center of mass. A "free body" analysis ignores forces internal to the body, but forces internal to the body can use up energy.

A.T.
I was trying to identify which athlete does more work per rep/stride.
Who can do more repetitions in a row?

Who can do more repetitions in a row?
No, who does more work per rep? Does the weight lifter do more work lifting the weighted bar off the ground than the runner during one stride. At first glance it seemed logical that a lifting 118Kg 1 meter of the ground would do more expend more energy, but the marathon runner is producing enough force to move 1 mile in less than 6 minutes. I was looking for a way to compare the two. Stephan Tashi gave me a decent answer to look at it based on caloric expenditure rather than force or work.

How can the marathon runner do more work in one stride than a weightlifter?

Anyway, once a weightlifter racks the bar, she or he has done no work as the displacement of the weight is 0.

Measuring the power output of a runner has been very very problematic. Try cycling instead. A power meter for cycling costs 800 euro. A power meter for a runner doesn't exist. You can't buy one even if you have a million dollars to spend.

I don't understand what your question is. On the one side we have a person doing one repetition. On the other we have thousands of repetitions.
In both the problem of efficiency is crucial. You can object to me saying the weightlifter does no net work. But if you consider the trajectory of the weight, it will be variable. Some people will have better technique than others and they can lift more weight, expending less energy.
The two systems of metabolism are also different, making a comparison impossible.

And in the end you have to consider what the muscles are doing. Not how much weight is displaced or how much distance is covered.

billy_joule
How can the marathon runner do more work in one stride than a weightlifter?

Anyway, once a weightlifter racks the bar, she or he has done no work as the displacement of the weight is 0.

Measuring the power output of a runner has been very very problematic. Try cycling instead. A power meter for cycling costs 800 euro. A power meter for a runner doesn't exist. You can't buy one even if you have a million dollars to spend.

I don't understand what your question is. On the one side we have a person doing one repetition. On the other we have thousands of repetitions.
In both the problem of efficiency is crucial. You can object to me saying the weightlifter does no net work. But if you consider the trajectory of the weight, it will be variable. Some people will have better technique than others and they can lift more weight, expending less energy.
The two systems of metabolism are also different, making a comparison impossible.

And in the end you have to consider what the muscles are doing. Not how much weight is displaced or how much distance is covered.

I specified only one stride therefore your argument concerning thousands to one does not hold. I never mentioned racking the bar either - imagine the bar is lifted and disappears instantaneously after having been moved through the complete rep if you must. A few comments above steven tashi gave a pretty good answer and understood my question. If you read his comments they may elucidate you to what I was considering. He also alluded to the idea that power could be calculated for the single stride be it there a physicist with the incentive to do such.

Who can do more repetitions in a row?
No, who does more work, or produces more force: the weightlifter lifting 118 kg 1 meter, or the marathon runner during one stride.

The weight i chose was arbitrary.

A.T.
No, who does more work per rep? Does the weight lifter do more work lifting the weighted bar off the ground than the runner during one stride. At first glance it seemed logical that a lifting 118Kg 1 meter of the ground would do more expend more energy, but the marathon runner is producing enough force to move 1 mile in less than 6 minutes.
Make up your mind, if you are considering the work during one stride, or during 1 mile.

Make up your mind, if you are considering the work during one stride, or during 1 mile.
You have misinterpreted this. The force produce per stride is directly related to the ability to move at such a high rate of speed - a sub 6 minute mile. 5280 feet per mile each stride is around 6'5"...

A.T.
rate of speed
I see, you just mean a certain speed, during that one stride. Now my question to you is: Can a weightlifter repeat the lifting continuously for 6 min. (lift,drop,lift,drop...), like the runner repeats the strides?

While exhaustion is not a direct measure of internal work done, you can still decide what requires more internal work if the exhaustion rate is decisively different. For example if the weight lifter can do the continuous lifting-dropping for only 30sec, it's quite probable that it requires more work than a stride that can be repeated for 6min.

Hmm, I thought this was in the biology section. If I knew that it wasn't I wouldn't have replied like I did.

gleem
It is estimated that the maximum rate of work that a human can maintain of an extended period of time is about 60 watts or about 1/10 hp. this is equivalent to lifting 6 kg i meter every second.

An runner can use about 1100 cal/hr at 16 km/hr. Note that one dietary cal is 1000 physical cal. that runner uses energy at a rate of about 1280 watts. Most of this energy is carried away in the perspiration and exhaled CO2 and H20 as heat. the actual work rate done is difficult to calculate because of the complex motion of constant changing accelerations and decelerations and rising and falling of the body and other motion but I think we can assume that it will be 60 watts

Try this. How many deep knee bends can you do in one minute? your power for doing work is Mass(kg)*dist(m)*9.8/60 watts. How many minutes can you keep this up? Your max output should be you first. depending on your mass about 300-400 watts.

When the weightlifter raises the bar, his muscles expend chemical energy, some of which is expended into the raising gravitation potential energy of the bar (the efficiency is not even close to perfect). When the bar is lowered, your muscles are unable to reabsorb the gravitational potential energy of the bar into chemical energy, so in effect, your muscles did all the work to move the bar up but did not reclaim that energy in moving it back down (that energy is instead dissipated, most likely as heat).

Merlin3189
If a marathon ends at the same place or elevation it began at, no work is done.

A weight lifter does no work.

Work = force on a body over a distance that results in an increase of potential energy of that body, no displacement no work.

What you want is calories burned, one is high force very short time, the other is low force very long time, use impulse to compair rates of thermodynamic work not kinetic potential.

If this is limited to a single stride of the runner what is the time per stride, then because the runner is already at spread the force is only that which maintaines that speed

A weight lifter is continuously accelerating the mass against gravity

Chicken or egg, who did more "what?" is silly because "what" is not comparable in that the two athletes cannot switch places.
A triathlon measures all players on the same scale. The winner output more energy over a shorter time.

Asking the corect question is critical. 'I-Robot'

A.T.
A weight lifter does no work.

Work = force on a body over a distance that results in an increase of potential energy of that body, no displacement no work.
So lifting the weight doesn't result in an increase of its potential energy ?

gleem
so in effect, your muscles did all the work to move the bar up but did not reclaim that energy in moving it back down (that energy is instead dissipated, most likely as heat).
In fact lowering the weight require energy to maintain the force supporting the weight as it is lowered.

If a marathon ends at the same place or elevation it began at, no work is done.

A weight lifter does no work.
the runner did work even though he ended up at the same elevation. He continually applied a force through a distance. the weight lifter likewise did work for the same reasons.
A weight lifter is continuously accelerating the mass against gravity
Not necessarily. Once the weigh start moving we just need to keep it moving to raise it.
o lifting the weight doesn't result in an increase of its potential energy ?
Of course it does. If the lifter releases the weight it falls using its potential energy to dent the floor when it hits,