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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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A flat uniform circular disk (radius = 2.00 m, mass = 1.00 ✕ 102 kg) is initially stationary. The disk is free to rotate in the horizontal plane about a friction less axis perpendicular to the center of the disk. A 40.0-kg person, standing 1.25 m from the axis, begins to run on the disk in a circular path and has a tangential speed of 2.00 m/s relative to the ground.

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0 = L for disk + L............... for runner

0 = Iω² - mv²r ...................they're opposite in direction

0 = (MR²/2)(ω²) - mv²r ................where is ω is angular speed which is required in part (a) of question

0 = [(1.00×10²kg)(2.00 m)² / 2](ω²) - (40.0 kg)(2.00 m/s)²(1.25 m)

0=200ω²-200

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ω = 1 rad/s

b.)

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The person's angular speed is  

v/r = (2.00 m/s) / (1.25 m) = 1.6 rad/s

As the person and the disk are moving in opposite directions, the person will run part of a revolution and the turning disk would complete the whole revolution.

(angle) + (angle disk turns) = 2π

(1.6 rad/s)(t) + ωt = 2π

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