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22 June, 09:10

A 68 kg hiker walks at 5.0 km/h up a 9% slope. The indicated incline is the ratio of the vertical distance and the horizontal distance expressed as percentage.

What is the necessary metabolic power?

Hint: You can model her power needs as the sum of the 380 W power to walk on level ground plus the power needed to raise her body by the appropriate amount. Assume that the efficiency of the body in using energy is 25%.

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  1. 22 June, 11:19
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    The power is calculated using the formula:

    Power = Work / Time

    where Work = Force * Distance, therefore:

    Power = Force * Distance / Time

    Power = Force * Velocity

    Converting the velocity in units of m/s:

    Velocity = (5km / h) (1000m / km) (1h / 3600s)

    Velocity = 1.39 m/s

    The force is equal to the y-component of the hikers weight:

    Force = Wy * g = W * sin θ * g

    Let us first find the angle θ. By definition the slope is equivalent to:

    slope = tan θ = ratio of vertical and horizontal distance

    tan θ = 0.09

    θ = 5.14˚

    Therefore, Force = 68 kg * sin (5.14˚) * 9.8 m/s^2

    Force = 666.4 * sin (5.14) = 59.73 N

    Calculating for power:

    Power = 59.73 N * 1.39 m/s = 82.96 W

    Since the hikers efficiency is 25%, to determine the metabolic power:

    Metabolic Power = 82.96 W / 0.25 = 331.83 watts
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