Physics Question: Who gave more effort? Calling all Numbers Geeks!

Runner B ran for a longer time, therefore did more work.

It's not rocket science. wrote:

Runner B ran for a longer time, therefore did more work.

It can't be that simple, tho... if you move an object (yourself) faster, are you doing more work? It takes more energy to move an object faster, not slower... which is why the weights of the objects (runners) matter...right?

I did more work having read your poorly phrased post

exhausted wrote:

I did more work having read your poorly phrased post

I asked for Numbers Geeks, not Grammar Nazis.

Don't lash out at me just because you never learned to count.

Next.

The first reply is at least partially correct. There is a tine component which you have ignored.

Doing no work against gravitational acceleration on a flat course.

Would be tough to quantify, though, as in a race it isn't the typical friction-free conditions of physics class.

Good morning class...

Class! STO-O-O-O-P!

Does everyone understand now why we will never make it back to the moon?

The sum of the forces of a mobile in uniform motion (regularly paced runner) is nought, thus F = ma = 0. However, there are internal forces that dissipate energy, it is about 1 kcal/km/kg in long distance running (+/- 10% due to running efficiency). Thus, the heavier runner produces more work (= energy) and (roughly) the same power (= energy output per unit of time) as the lighter one.

The faster runner always does more.

He is faster and not fat.

thejeff wrote:

Work = Force x Distance, so W = F x (13.1mi, or 21. 08km)

So, what is Force? Mass times Acceleration.

So, Work = (M x a) x 13.1 miles.

This is where I get lost, if I am even barking up the right tree... how to quantify acceleration? Is it even necessary?

Is there an easier way to think about this?

m: mass of the runner

a: acceleration of the runners center of mass, while he's applying force (aka while he has a foot on the ground).

d: displacement of the runner's center of mass over the course of one footstrike

vectors a and d aren't in the same direction, so for accel, we really want the component of a that's in the direction of d.

so m*a*d would be the work of one footstrike. multiply that by the number of steps the runner took for the total work done.

thejeff wrote:

Runner A: Speedy McLightweight: 135 lbs, finished in 1:12:00.

Runner B: Dee Lineman: 200 lbs, finished in 1:35:00.

So, who gave more effort?

I assume the question I need to ask is: Who did more WORK?

If you did manage to estimate work for both runners, I suspect you'll find runner B did more work. Over the same distance, the fat guy is probably always going to do more work, regardless of his time.

The problem is that work doesn't tell you much without knowing time (we're only holding distance fixed). Consider 2 guys climbing up a ladder. If they weigh the same amount, and they climb up to the same height, they've done the same amount of work, even if one of them was 10x faster.

"Give me a lever long enough and a fulcrum on which to place it, and I shall move the world." Our situation is similar...give me enough time and I can move mountains.

This ^ is the best answer.

For all practical purposes the heavier runner will always do more work to cover the same ground.

However, work (physics definition) definitely is not the same thing as effort (common understanding). 'Who gave more effort?' might reasonably be understood as 'who came closest to maxing out their potential for that distance on that day?' This is not really a question of physics at all.

loqueelvientoajuarez wrote:

The sum of the forces of a mobile in uniform motion (regularly paced runner) is nought, thus F = ma = 0. However, there are internal forces that dissipate energy, it is about 1 kcal/km/kg in long distance running (+/- 10% due to running efficiency). Thus, the heavier runner produces more work (= energy) and (roughly) the same power (= energy output per unit of time) as the lighter one.

Mainly correct. But there's also some external friction due to air resistance, shoes slipping, clothing, etc.

thejeff wrote:

Is there an easier way to think about this?

Probably. Assuming you are indeed looking to measure 'work' as defined by physics as a measurement of energy spent (Joules), rather than 'effort' which is a quantity you would have to define.

You cannot simply use E=Fs (work = force x distance). Energy consumed during running is dominated by the energy spent overcoming losses due to friction. The energy spent accelerating to race pace is tiny compared to the energy spent maintaining race pace over the race distance.

It is an oversimplification, but you can model total energy consumed with a linear function of E = mass x K (where K is some constant) i.e. the heavier runner consumes more energy per mile.

This simplification comes from looking at measurements of oxygen consumption and respiratory quotient from subjects on a treadmill running at various speeds. With oxygen consumption and respiratory quotient you can work out kcal consumption (kcal is a measurement of energy and you can convert it to Joules).

Lighter and faster runners do less work, requiring fewer calories. This is actually a benefit.

The heavier runner always wins the battle of physics provided the distance is the same.

Alan

Runningart2004 wrote:

Lighter and faster runners do less work, requiring fewer calories. This is actually a benefit.

The heavier runner always wins the battle of physics provided the distance is the same.

Alan

This actually came up in our conversation, lol. Initially, the heavier runner considered it (the possibility that he had done more work/effort) something of a Badge of Honor. Put in different terms, though, maybe the "less efficient" runner shouldn't be proud of being less efficient, lol

Hawking wrote:

The first reply is at least partially correct. There is a tine component which you have ignored.

What time component? Other than the finishing times I included?

This sounds like one of those discussions where a "big boned" person tries to make their performance seem like it is better than the winner.

The more interesting question is who spends most energy per unit of mass.