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lana66690 [7]
3 years ago
14

While running, a person dissipates about 0.60 J of mechanical energy per step per kilogram of body mass. If a 61 kg person devel

ops a power of 65 W during a race, how fast is the person running? Assume that a running step is 1.5 m long.
Physics
1 answer:
liraira [26]3 years ago
6 0

Answer:

2.66m/s

Explanation:

information we have

power: 65W

work per step per kilogram: 0.60J

mass: 61kg

length of a running step: 1.5m

---------------

the formula for power is:

P=\frac{W}{t}

where W is the work and t is time.

time is also defined as: t=\frac{distance}{velocity}=\frac{d}{v}

so substituting this into the formula for power we get:

P=\frac{W*v}{d}

where v is the velocity we are looking for, d is the distance per step: d=1.5m, W is the work per step and P is power P=65W.

we know that the work per step per kilogram is:

0.60J

so to find the work per step of his whole body we need to multiply the 0.60J by the 61 kilograms of his mas:

W=0.60J*61kg\\W=36.6Jthis is the work per step of the person.

So now we can calculate the velocity using the formula for power

P=\frac{W*v}{d}

clearing for v:

v=\frac{P*d}{W}\\

and substituting known values:

v=\frac{(65W)(1.5m)}{36.6J}= 2.66m/s

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