While running, a person dissipates about 0.60 J of mechanical energy per step per kilogram of body mass. If a 61-kg person develops a power of 75 W during a race, how fast is the person running?
.60*61*steps=75*time
solve for steps/time
To find the speed at which the person is running, we need to use the formula for power:
Power = Work done / Time
We are given that the person develops a power of 75 W during the race. Let's assume the time for one step is 't' seconds, and the person dissipates about 0.60 J of mechanical energy per step per kilogram of body mass.
The work done in one step is given by:
Work done per step = Mechanical energy dissipated per step per kg * Mass
Substituting the given values:
Work done per step = 0.60 J/step/kg * 61 kg
Now, we can find the time for one step:
Power = Work done per step / Time
75 W = (0.60 J/step/kg * 61 kg) / t
Simplifying:
75 W = 0.60 J/step * 61 kg / t
To find 't', rearrange the equation:
t = (0.60 J/step * 61 kg) /75 W
Now, we can calculate the value of 't'.
Substituting the given values, we get:
t = (0.60 J/step * 61 kg) /75 W
t ≈ 0.488 seconds per step
Since we are assuming the time is for one step, the speed of the person can be calculated by dividing the distance covered in one step by the time taken for one step.
To find the distance covered in one step, we need to know the length of the step or the stride length.
Let's assume the stride length is 's' meters. Then the speed of the person can be calculated as:
Speed = Distance / Time
Speed = s / t
Now, if you know the length of the person's step or stride length, you can substitute the value to find the speed.