Power consumption of a human running

[arkturus]

Homework Statement

If a 70kg man is running 3 m/s horizontally, how many watts is he consuming?

Homework Equations

W = N-m/s
N = mass*acceleration

The Attempt at a Solution

I would assume that in order to get the force in N one would use the gravitational constant of the Earth, but the man is moving in a horizontal line. Regardless, he is technically using work to move 'up' since his center of mass is going slightly up and down. How do I account for this, however?

Thank you.

 

[NascentOxygen]

I would assume that in order to get the force in N one would use the gravitational constant of the Earth, but the man is moving in a horizontal line. Regardless, he is technically using work to move 'up' since his center of mass is going slightly up and down. How do I account for this, however?

Unless you were given typical data for the energy (or force) demanded of a runner I don't think you are going to be able to answer this. Sure, he does lift his CoM during each step, but that energy is returned when he allows it to then fall, so no nett energy expenditure there.

I vaguely recall this same or a similar question from some months back, but I may be imagining things. https://www.physicsforums.com/images/icons/icon6.gif

 

[CWatters]

What he said. You do not have enough information to calculate the power.

If it was 3m/s vertically that would be a different matter. In that case the man is gaining Potential Energy at a known rate so you could calculate his minimum power output.

If the problem is homework or from a book perhaps type it in word for word?

 

[CWatters]

he is technically using work to move 'up' since his center of mass is going slightly up and down.

however what he expends going "up" he gets back going "down". So it's only the "losses" that he incurs in the process that he has to provide. Plus air resistance etc.

In case it helps.. I remember reading that a fit person can produce about 250W for sustained periods. That's the sort of figure I think you have to assume when designing a man powered aircraft. Apparently it's easier to teach a racing cyclist to fly a plane than to train a pilot to produce the required power.

 

[Nickie]

I would first clarify the units being used. The correct unit for power is watts (W), not N-m/s. N-m/s is the unit for work, which is the amount of energy transferred when a force of 1 newton is applied over a distance of 1 meter.

To calculate the power consumption of the man running, we first need to calculate the force he is exerting. This can be done using Newton's second law, which states that force (F) is equal to mass (m) multiplied by acceleration (a). In this case, the man's mass is given as 70kg and his acceleration is 0 m/s^2 (since he is running at a constant velocity), so the force he is exerting is 0 N.

Next, we need to calculate the work he is doing. As mentioned earlier, work is equal to force multiplied by distance. In this case, the man is moving horizontally, so the distance he is covering is 3 meters. Therefore, the work he is doing is 0 N * 3 m = 0 N-m.

Finally, we can calculate the power consumption by dividing the work by the time it takes to complete it. The time it takes for the man to run 3 meters at a velocity of 3 m/s is 1 second. Therefore, the power consumption is 0 N-m / 1 s = 0 watts.

In conclusion, the man running at a velocity of 3 m/s is consuming 0 watts of power since he is not exerting any force or doing any work. This may seem counterintuitive, but it is because he is moving at a constant velocity and not accelerating. If he were to accelerate or run up a hill, he would be exerting a force and consuming power.