A) The change in internal chemical energy is ![1.15\cdot 10^7 J](https://tex.z-dn.net/?f=1.15%5Ccdot%2010%5E7%20J)
B) The time needed is 1 minute
Explanation:
First of all, we start by calculating the power output of you and the bike, given by:
![P=Fv](https://tex.z-dn.net/?f=P%3DFv)
where
F = 80 N is the force that must be applied in order to overcome friction and travel at constant speed
v = 8.0 m/s is the velocity
Substituting,
![P=(80)(8.0)=640 W](https://tex.z-dn.net/?f=P%3D%2880%29%288.0%29%3D640%20W)
The energy output is related to the power by the equation
![P=\frac{E}{t}](https://tex.z-dn.net/?f=P%3D%5Cfrac%7BE%7D%7Bt%7D)
where:
P = 640 W is the power output
E is the energy output
is the time elapsed
Solving for E,
![E=Pt=(640)(1800)=1.15\cdot 10^6 J](https://tex.z-dn.net/?f=E%3DPt%3D%28640%29%281800%29%3D1.15%5Ccdot%2010%5E6%20J)
Since the body is 10% efficient at converting chemical energy into mechanical work (which is the output energy), this means that the change in internal chemical energy is given by
![\Delta E = \frac{E}{0.10}=\frac{1.15\cdot 10^6}{0.10}=1.15\cdot 10^7 J](https://tex.z-dn.net/?f=%5CDelta%20E%20%3D%20%5Cfrac%7BE%7D%7B0.10%7D%3D%5Cfrac%7B1.15%5Ccdot%2010%5E6%7D%7B0.10%7D%3D1.15%5Ccdot%2010%5E7%20J)
B)
From the previous part, we found that in a time of
t = 30 min
the amount of internal chemical energy converted is
![E=1.15\cdot 10^7 J](https://tex.z-dn.net/?f=E%3D1.15%5Ccdot%2010%5E7%20J)
Here we want to find the time t' needed to convert an amount of chemical energy of
![E'=3.8\cdot 10^5 J](https://tex.z-dn.net/?f=E%27%3D3.8%5Ccdot%2010%5E5%20J)
So we can setup the following proportion:
![\frac{t}{E}=\frac{t'}{E'}](https://tex.z-dn.net/?f=%5Cfrac%7Bt%7D%7BE%7D%3D%5Cfrac%7Bt%27%7D%7BE%27%7D)
And solving for t',
![t'=\frac{E't}{E}=\frac{(3.8\cdot 10^5)(30)}{1.15\cdot 10^7}=1 min](https://tex.z-dn.net/?f=t%27%3D%5Cfrac%7BE%27t%7D%7BE%7D%3D%5Cfrac%7B%283.8%5Ccdot%2010%5E5%29%2830%29%7D%7B1.15%5Ccdot%2010%5E7%7D%3D1%20min)
Learn more about power and energy:
brainly.com/question/7956557
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