It is assumed that while running the most of the work done i

It is assumed that while running the most of the work done is by leg muscles accelerating each leg to running speed v and then decelerating it to zero velocity as one leg is brought to rest and another one is accelerated. The work in accelerating and decelerating the leg of mass m (usually 14% of body mass) is fraction numerator m v squared over denominator 2 end fraction, so the total work during each stride is m v squared. Typical muscle efficiency (converted to work energy) is 20%. Compute power (in Watts) required to be generated by a 50-kg person running at 3 space fraction numerator m over denominator s e c end fraction with a step length 90 cm. Present only numeric portion of your answer.

Solution

Using the equation of motion:

v^2 = u^2 + 2as

So,

3^2 = 0^2 + 2*a*0.9

So, a = 5 m/s2

Now, using the equation:

v = u +at

So, 3 = 0 + 5*t

So, t = 0.6 s

Now, work done during each stride:

W = m*v^2 = (0.14*50)*3^2 = 63 J

So, power to be generated = (W/t)/0.2

So, P = (63/0.6)/0.2

= 525 W <-------answer