A 68 kg hiker walks at 5.0 km/h up a 7% slope. The indicated incline is the rati

Question

A 68 kg hiker walks at 5.0 km/h up a 7% 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%.

Express your answer to two significant figures and include the appropriate units.

Explanation / Answer

Power = Work ÷ time
Work = Force * distance
Power = Force * distance ÷ time
Power = Force * velocity

Let’s convert the velocity to m/s. 1 km = 1000 m, 1 h = 3600 s, 1 km/h = 1000/3600 = 5/18 m/s
v = 5 * 5/18 = 25/18
This is approximately 1.39 m/s.

The force is equal to the component of the hiker’s weight that is parallel to the slope.
Force parallel = 68 * 9.8 * sin = 666.4 * sin
Since the slope is the ratio of the vertical and horizontal distances, the slope is equal to the tangent of the angle.

Tan = 0.07
= tan^-1 0.07
This is approximately 4.00.
Sin = sin (tan^-1 0.07)
Force parallel = 666.4 * sin (tan^-1 0.07) = 46.534 N

Power = 46.534 * 25/18 = 64.630 watts
Since her efficiency is 25%, to determine the metabolic power, multiply by 4
Power = 4 * 64.630 = 258.52 watts

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