A) The change in internal chemical energy is [tex]1.15\cdot 10^7 J[/tex]
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:
[tex]P=Fv[/tex]
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,
[tex]P=(80)(8.0)=640 W[/tex]
The energy output is related to the power by the equation
[tex]P=\frac{E}{t}[/tex]
where:
P = 640 W is the power output
E is the energy output
[tex]t = 30 min \cdot 60 = 1800 s[/tex] is the time elapsed
Solving for E,
[tex]E=Pt=(640)(1800)=1.15\cdot 10^6 J[/tex]
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
[tex]\Delta E = \frac{E}{0.10}=\frac{1.15\cdot 10^6}{0.10}=1.15\cdot 10^7 J[/tex]
B)
From the previous part, we found that in a time of
t = 30 min
the amount of internal chemical energy converted is
[tex]E=1.15\cdot 10^7 J[/tex]
Here we want to find the time t' needed to convert an amount of chemical energy of
[tex]E'=3.8\cdot 10^5 J[/tex]
So we can setup the following proportion:
[tex]\frac{t}{E}=\frac{t'}{E'}[/tex]
And solving for t',
[tex]t'=\frac{E't}{E}=\frac{(3.8\cdot 10^5)(30)}{1.15\cdot 10^7}=1 min[/tex]
Learn more about power and energy:
brainly.com/question/7956557
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