what is the WORK done...

[paul]

...when a man with a mass of 90kg runs 100m at a velocity of 10m/s?

 

what is the work done when the same man walks 100m at a velocity of 1m/s?

 

(this isn't a homework question; i'm trying to grasp the concept)

[Cap'n Refsmmat]

Work is, in the most simplified form, force times distance. So all you need to do is find the force. And F=ma. So what would that give you?

 

(Hint: is he accelerating?)

[paul]

thanks cap'n.

 

so, man walking;

 

a = delta v/delta t

a = 1m/s/100

a = 1/100m/s^2

 

F=ma

F=90 x 1/100

F= 0.9N

 

w=Fd

w=0.9x100

w= 90J

 

man running;

 

a=delta v / delta t

a=10/10

a=1m/s^2

 

F=ma

F=90x1

F=90N

 

w=Fd

w=90x100

w=9000J

 

but that can't be right? walking = 90 J ; running = 9000J?

 

i thought it took the same energy to run over a distance as it did to walk, no?

[D H]

The work in both cases is zero (assuming the person comes back to rest in each case, that is).

[paul]

thanks DH.

 

but can we assume that the person continues running/walking beyond the 100m, but only measure the work over the 100m?

 

(and ignore friction)

[D H]

In that case, the runner obviously performs more work. Since there is no friction, all of the energy expended by the runner/walker goes into changing the person's kinetic energy. Who crosses the finish line with more kinetic energy?

[paul]

the runner crosses the finishing line with more kinetic energy?

 

but i'm thinking of the first example i've been taught for w=Fd;

 

pushing a lawnmower with a force of 90N over 1000m = 90,000J

 

so i noticed that time didn't come into it. it didn't seem to matter whether it was done quickly or slowly; it just seems to say that to move the lawnmower over 1000m with a force of 90N would take 90,000J?

 

ah, but hold on... to push it with a force of 90N for a person of a particular mass would get the job done in a particular time. to do the job more quickly would take a greater force from the same person (F=ma) ?

 

am i on the right track here..?

[Cap'n Refsmmat]

Yes. To get the runner to accelerate to the higher speed, he must accelerate more, and (assuming he has the same mass as the walker) that takes a greater force over that distance, and hence more work.

[Sione]

...when a man with a mass of 90kg runs 100m at a velocity of 10m/s?

 

what is the work done when the same man walks 100m at a velocity of 1m/s?

 

 

so, man walking;

 

a = delta v/delta t

a = 1m/s/100

a = 1/100m/s^2

 

you say velocity, but calculate acceleration.

 

to answer your question, work is most certainly not zero and is most definitely not the same for running and walking. perhaps if there was no gravity, but then you would be floating.

 

energy is the ability to do work or to cause change, so from that you should know that you indeed perform work in such exercise, even if you run on a treadmill.

 

 

but can we assume that the person continues running/walking beyond the 100m, but only measure the work over the 100m?

(and ignore friction)

 

you must not ignore friction if you are interested in calculating work, the friction is what makes you repel and move in a first place. air/ground friction and gravity is what you work against.

 

when running, you lift your knees higher and with more acceleration, so you should be performing more work per unit time.

 

people also can do work when rotating an object. for example, a person who unscrews the lid of a milk jug does work. in this case, the resistance is the force of friction that the screw threads of the jug exert against the lid.

 

 

no work is done when you hold your hand stationary against gravity, in a classical sense. but, it will get you tired and you will use extra energy to perform it. having energy as an ability to do work you know that in fact you did perform some work, only the things that were displaced were internal, like muscle contraction, movement within the fibers, heart-rate, blood pressure, temperature...

[Sisyphus]

Basically there's not enough information. In theory, nothing you mention in the initial question requires any work at all. Merely having a velocity or travelling a distance does not inherently require work. (In contrast, acceleration or an increase in height would, but not if you slow back down or return to your original height.) In real life, however, though there are lots of other things going on: friction, air resistance, internal muscle action, etc. Overcoming these things does require energy to be expended, but you can't tell exactly how much without a much more complicated analysis.

[Sione]

After reading some research I have to express my surprise to find out their results show positive work is actually close to negative work. Still, air friction and joint friction will guarantee net positive work for any human motion.

 

Muscles do more positive than negative work in human locomotion: http://jeb.biologists.org/cgi/content/full/210/19/3361

 

That does not make sense to me because muscles are always in tension whether knee is going up or down, so i thought that resistance will cause positive work to be much greater than any negative work.

 

 

In the light of that I'd like to expand. It is obviously very important to recognize the direction of the force and that of displacement. We can have positive and negative work. Energy is used to do work on an object, exerting a force through a distance and this force is usually against something:

 

1.) Work against fundamental forces. Gravitational attraction, electromagnetic and nuclear forces.

 

2.) Work against friction or drag. Friction is always present when two objects are in contact with each other and is always a force in the opposite direction of the applied force.

 

3.) Work against inertia. Since inertia is an objects resistance to change of motion, it naturally follows that this would resist forces acting upon it.

 

 

Now I have a question. What kind of work is the one against inertia, can it be negative and how to recognize it. Here is a very popular example with two interpretations, which one is true?

 

 

Carrying a heavy box

 

Most of the textbooks say that this is not work, because the force of gravity is perpendicular to your motion, while some say moving the box across the room is work against the inertia of the box and lifting the box up is work against the resistive force of gravity.

Edited January 15, 2009 by Sione

[Pete]

...when a man with a mass of 90kg runs 100m at a velocity of 10m/s?

 

what is the work done when the same man walks 100m at a velocity of 1m/s?

 

(this isn't a homework question; i'm trying to grasp the concept)

 

The work done on the body is zero since the force on the body (only force acting here is grafvity) is perpendicular to the displacement (F*dr = 0 where "*" = dot product). Think of sliding a body over a surface of zero friction - no work is done there either. The runner does no work agains friction either (for the most part anyway).

 

However there is work being done inside the body in terms of biochemical reactions (muscle contractions etc). That's why we get tired when we run and even when all we do is press our hands together or stand.

 

3.) Work against inertia. Since inertia is an objects resistance to change of motion, it naturally follows that this would resist forces acting upon it.

If there is a non-zero amount of work done on a then the velocity of the body changes. The work-energy theorem tells us that the work done on a body by conservative forces equals the change in the kinetic energy of the body.

Now I have a question. What kind of work is the one against inertia, can it be negative and how to recognize it. Here is a very popular example with two interpretations, which one is true?

Positive work acclerates the body increasing the bodies kinetic energy. Negative work slows the body down thus decreasing the bodies kinetic energy.

Carrying a heavy box

 

Most of the textbooks say that this is not work, because the force of gravity is perpendicular to your motion, ...

That is correct.

...while some say moving the box across the room is work against the inertia of the box and lifting the box up is work against the resistive force of gravity.

If you're asking if work is done to move the body across the room then the answer is no. If you're asking if work is done ti life the body then the answer is yes. Those other texts are talking about the entire process of lifting and moving. The net result is a change in the bodies gravitational potential and any change in kinetic energy that may arise depending on how the body is moved (e.g. from a state of rest to a state of rest or from a state of rest to a state of motion etc.)

Edited January 16, 2009 by Pmb

[Sione]

The work done on the body...

 

That is a good point, to make a difference between "work done" and "work done on the body". I think when considering human performance it is natural to assume the question is about "work done by the body" as to be able to find energy consumed. The way I saw the question is in the sense of energy loss - will I loose more weight by running or walking every day certain distance.

 

 

If you're asking if work is done to move the body across the room then the answer is no. If you're asking if work is done ti life the body then the answer is yes. Those other texts are talking about the entire process of lifting and moving.

 

Yes, thank you. Unfortunately, if we have some human as a part of the system most people would assume, I think, it concerns the work that goes inside the body and how much energy it takes to do it.

 

 

Another question:

Human person walks some distance with constant velocity, calculate:

 

a.) work against inertia

b.) work against gravity

c.) work against friction

d.) total work done by the human

e.) total work done on the human

f.) energy exhausted from the human

 

 

 

 

 

===================================

 

Addendum:

Nonconservative forces other than friction include tension, compression and drag. Inertia as well?. Anyway, making displacement against these forces will always cause positive work. Negative work can be done only against conservative forces like gravity.

 

When you lift your knee you are doing positive work against gravity.

When you lift your knee gravity is doing negative work on your knee.

 

When you let your knee fall you are doing negative work "against" gravity.

When you let your knee fall gravity is doing positive work on your knee.

 

 

Work is done by a force. To define problem properly we need to name that single 'applied force' and object it is acting on. By introducing complex system such as human being we are unable to name that force because there are many forces involved, forces that move knee, elbow, shoulder...

 

Question should only involve one applied force, in a form: What is work done by FORCE on OBJECT. If we really wanted to know work done ON the human, we would need to specify what EXTERNAL force are we talking about, in some form of:

 

What is work done by 'gravity force' ON human.

(zero, force vector is perpendicular to the displacement)

 

or

 

What is work done by 'air friction force' ON human.

(negative non zero, force vector is in opposite direction to the displacement)

 

 

 

...however

 

What is work done by 'compound human force' AGAINST air friction

(positive non zero, force vector is in the direction of the displacement)

Edited January 16, 2009 by Sione
Consecutive post/s merged.