Steady state energy vs. energy rate

[Bill Foster]

I went for a run and measured time and distance. I wanted to estimate how many calories I used.

Suppose a ran a distance $$x$$ in an amount of $$t$$ time.

if my mass is $$m$$, then my stead state average energy would be

$$E=\frac{1}{2}m\frac{\Delta{x}^2}{\Delta{t}^2}$$

But what is the rate at which I am using energy?

Or what is the total energy used in either distance $$x$$ or time $$t$$?

Total energy used, or work, can be gotten from $$W=Fx$$, and the rate of energy used from $$P=Fv$$. But I don't know what the force $$F$$ is.

 

[Shooting Star]

If you stand still for one hour at a stretch, you'll probably be exhausted. Our body doesn't use or conserve energy quite like the sliding blocks or rolling balls of elementary mechanics.

The average force you have to overcome during running comes from various sources. One is obviously the air resistance. Another is the friction between muscles in your body -- the two legs don't act like double pendula. You also move your arms and other parts of the body relative to each other.

But the most significant energy loss would be this way: with every step, your centre of gravity rises and falls, and the co-efficient of restitution with the ground is not unity. So, with every step energy is lost and to bring back the CG to the same height, you have to expend energy. That's why making shoes for runners has become such a science -- the more spring your shoe has, the less energy you spend.

Think about it and I'm sure you'll find other sources of spending energy. It won't be very easy to find the average force F.

 

[charng]

I would first clarify the units being used in this scenario. For distance, I would use meters (m) and for time, I would use seconds (s). For mass, I would use kilograms (kg).

Next, I would explain that steady state energy refers to the average energy output over a period of time, while energy rate refers to the amount of energy used per unit of time. In this case, the steady state energy would be the average energy used during the entire run, while the energy rate would be the amount of energy used per second during the run.

To estimate the total energy used, we can use the equation W=Fx, where F is the force applied (in Newtons) and x is the distance traveled (in meters). However, since we do not have information about the force applied during the run, we cannot accurately calculate the total energy used.

To estimate the rate of energy used during the run, we can use the equation P=Fv, where F is the force applied and v is the velocity (in meters per second). Again, without knowledge of the force applied, we cannot accurately calculate the energy rate.

In order to accurately estimate the total energy used and the energy rate during the run, we would need to measure the force applied during the run. This can be done using a device such as a heart rate monitor or a fitness tracker that can track the force of each step taken. By combining this information with the distance and time data, we can calculate the total energy used and the energy rate during the run.