While running, a person dissipates about 0.60 J of mechanical energy per step per kilogram of body mass. If a 62 kg person develops a power of 67 W during a race, how fast is the person running? (Assume a running step is 1.5 m long.)
A 62 kg person produces 0.60*62 = 37.2 J of work per step (1.5 m). That is 24.8 J per meter.
Power in Watts (J/s) is V (m/s)*24.8 J/m
67 = 24.8 V
V = 2.7 m/s
thank you so much drwls
To find the speed at which the person is running, we need to use the relationship between power, work, and time.
Let's break down the problem and find the solution step by step:
1. We are given that a person dissipates about 0.60 J of mechanical energy per step per kilogram of body mass.
This means for each step the person takes, they dissipate 0.60 J of energy per kg of body mass.
2. The person's mass is 62 kg.
3. The person develops a power of 67 W during the race.
Power is defined as the rate at which work is done, so if the person's power is 67 W, they are doing 67 J of work per second.
4. We'll use the equation P = W/t, where P is the power, W is the work, and t is the time.
Rearranging the equation gives us W = P * t.
5. Considering that each step dissipates 0.60 J of energy per kg of body mass, we can write the work done for one step as:
Work = 0.60 J/kg * 62 kg = 37.2 J.
6. The length of each step is given as 1.5 m.
To find the time it takes to complete one step, we need to use the equation v = d/t, where v is the velocity, d is the distance, and t is the time.
7. Rearranging the equation gives us t = d/v.
8. Substituting the given values, we get t = 1.5 m / v.
Now, combining steps 4, 7, and 8:
Work = P * t,
37.2 J = 67 W * t,
t = 37.2 J / 67 W.
9. Substituting the value of t into the equation t = 1.5 m / v, we get:
37.2 J / 67 W = 1.5 m / v.
Finally, we can solve for v, the speed at which the person is running.
10. Rearranging the equation gives us v = (1.5 m * 67 W) / 37.2 J.
Calculating this expression will give us the speed at which the person is running.