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? Assume a running step is 1.5 m long.
70 J/s = (V/1.5)step/s*(0.6 J/step kg)*60 kg
Solve for V in meters/s
V = 70*1.5/(0.6*60) = 2.9 m/s
That is a pretty slow speed for a runner. It's roughly 9 minutes miles... more like jogging.
Thank you!
To determine the speed of the person running, we need to calculate the total energy dissipated per second and then divide it by the power.
First, let's calculate the total energy dissipated per second. Given that a person dissipates 0.6 J of mechanical energy per step per kilogram of body mass, we can multiply this value by the person's body mass and the number of steps taken per second.
Number of steps per second can be calculated by dividing the person's speed by the step length, which is 1.5 m.
Number of steps per second = Speed / Step length = Speed / 1.5 m
Since we don't know the speed yet, we'll leave it as 'Speed' in the equation for now.
Now the energy dissipated per second can be calculated as:
Energy dissipated per second = 0.6 J/step/kg * body mass * number of steps per second
Next, we can calculate the speed by dividing the power by the energy dissipated per second.
Speed = Power / Energy dissipated per second
Plugging in the given values:
Speed = 70 Watts / Energy dissipated per second
Now, substituting the previously calculated values:
Speed = 70 Watts / [0.6 J/step/kg * 60 kg * (Speed / 1.5 m)]
To solve this equation for Speed, we can simplify it:
Speed = 70 * 1.5 / (0.6 * 60) m/s
Calculating further:
Speed = 1.75 m/s
Therefore, the person is running at a speed of 1.75 m/s during the race.