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Viktor [21]
2 years ago
11

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 di

stance 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%.
Physics
1 answer:
expeople1 [14]2 years ago
6 0

The power is calculated using the formula:

Power = Work / Time

where Work = Force * Distance , therefore:

Power = Force * Distance / Time

Power = Force * Velocity<span>


Converting the velocity in units of m/s:</span>

Velocity = (5km / h) (1000m / km) (1h / 3600s)<span>
Velocity = 1.39 m/s 

The force is equal to the y-component of the hikers weight:</span>

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<span>
Force = 666.4 * sin (5.14) = 59.73 N 

</span>

<span>Calculating for power:
<span>Power = 59.73 N * 1.39 m/s = 82.96 W
Since the hikers efficiency is 25%, to determine the metabolic power: 
<span>Metabolic Power = 82.96 W / 0.25 = 331.83 watts </span></span></span>
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Distance of the wire from the center of the coil, d = 20 cm = 0.2 m

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B_{2} = \frac{\mu_{0}I }{2\pi(2d)) } \\B_{2} = \frac{\mu_{0}I }{4\pi d } \\

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Change in the magnetic field, ΔB = B₂ - B₁ = 0.00001725 - 0.0000345

ΔB = -0.000001725

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Radius, r = 0.00625 m

A = π* 0.00625²

A = 0.0001227 m²

Δ∅ =  -0.000001725 * 0.0001227

Δ∅ = -211.6575 * 10⁻¹²

E = -N (Δ∅)/Δt

E = -5\frac{-211.6575 * 10^{-12} }{4.70} \\E = 225.17 * 10^{-12} V

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I = E/R

I = \frac{225.17 * 10^{-12} }{3.25 * 10^{-6} }

I = 0.0000693 A

I = 69 .3 * 10⁻⁶A

I = 69.3  μA

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