Question

While running, a person dissipates about 0.6 J of mechanical energy per step per kilogram of body mass. If a 60-kg person runs with a power of 70 Watts during a race, how fast is the person running

Answer 1

Complete question is: While running, a person dissipates about 0.60 J of mechanical energy per step per kilogram of body mass. If a 60-kg person develops a power of 70 W during a race, how fast is the person running? (Assume a running step is 1.5 m long).

Answer: The person running at a speed of 2.91 m/s.

Explanation:

Given: Mass of runner = 60 kg

Runner dissipates = 0.6 J/kg per step

Average power = 70 W

1 step = 1.50 m

Energy dissipated by the runner is as follows.

$\Delta E_{step} = 0.60 \times 60\\= 36 J$

Formula used to calculate the value of one step 'S' is as follows.

$\frac{S}{\Delta t} = \frac{P_{avg}}{\Delta E_{step}} = \frac{70}{36}\\= 1.94\\S = 1.94 \Delta t$

It is known that average velocity is equal to the total distance divided by time interval.

So, total distance for the given situation is as follows.

$d = S \times 1.5$

Hence, speed of the person is calculated as follows.

$v_{avg} = \frac{d}{\Delta t}\\= \frac{S \times 1.5}{\Delta t}\\= \frac{1.94 \Delta t \times 1.5}{\Delta t}\\= 2.91 m/s$

Thus, we can conclude that the person running at a speed of 2.91 m/s.