Question

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 65 W during a race, how fast is the person running? Assume that a running step is 1.5 m long.

Answer 1

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

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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:

$W=0.60J*61kg\\W=36.6J$this 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:

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