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 78 W during a race, how fast is the person running? (Assume a running step is 1.5 m long.)
.6 j/(step kg) *60 kg = 36 j/step
36 j/step *1 step/1.5 m = 24 J/m
24 J/m * v m/s = 24 v J/s or 24 v watts
24 v watts = 78 watts
v = 78/24 = 3.25 meters/second
4PPL35 4R3 F0R N00B5
4PPL35 4R3 F0R N0085
To find the speed at which the person is running, we need to use the power developed by the person and the dissipated mechanical energy per step.
The power developed during the race is given as 78 W. Power is defined as the rate at which work is done, so we can express it as:
Power = Work / Time
We can rearrange this equation to solve for work:
Work = Power × Time
Now, we need to determine the work done per step. The question states that a person dissipates about 0.60 J of mechanical energy per step per kilogram of body mass. Since the person weighs 60 kg, the work done per step can be calculated as:
Work per step = Dissipated energy per step per kg × Mass of person
Work per step = 0.60 J/step/kg × 60 kg
Next, we need to find the time it takes for the person to complete one step. Since we know the length of the step is 1.5 m, we can use this information to calculate the time:
Time = Distance / Speed
Speed = Distance / Time
Given that the length of one step (distance) is 1.5 m, we need to find the time it takes to complete one step. We'll use the speed formula to solve for this.
Now, to find the speed, we can substitute the values of work per step and time into the equation for speed:
Speed = Distance / Time
Speed = 1.5 m / Time
Finally, we can substitute the values of work per step, power, and mass into the equation for time:
Work per step = Power × Time
0.60 J/step/kg × 60 kg = 78 W × Time
Now, solve for Time:
Time = (0.60 J/step/kg × 60 kg) / 78 W
Once you find the value of Time, substitute it back into the equation for speed:
Speed = 1.5 m / Time
Calculating the final value will give you the speed at which the person is running.