Given,
The power consumed by a brain, P=22 W
The energy per bar, E=280 calories=280×4184=1171.52 kJ
The mass of a milk container, m=3.6 kg
The power output of the arm, P₀=22 W
The distance through which the container needs to be lifted, d=1.0 m
a)
The power is given by,
[tex]P=\frac{E}{t}[/tex]Where t is the time.
On substituting the known values in the above equation,
[tex]\begin{gathered} 22=\frac{1171.52\times10^3}{t} \\ \Rightarrow t=\frac{1171.52\times10^3}{22} \\ =53250\text{ s} \end{gathered}[/tex]That is,
[tex]\frac{53250}{3600}=14.79\text{ hr}[/tex]Therefore one snicker bar can power the brain for 14.79 hr
b)
The power output can also be calculated using the formula,
[tex]\begin{gathered} P=F\times v \\ =mg\times v \end{gathered}[/tex]Where F is the force applied by the container on the arm, v is the rate at which the container must be lifted, and g is the acceleration due to gravity.
On substituting the known values,
[tex]\begin{gathered} 22=3.6\times9.8\times v \\ v=\frac{22}{3.6\times9.8} \\ =0.62\text{ m/s} \end{gathered}[/tex]Thus the rate at which the milk container must be lifted is 0.62 m/s
c)
The rate at which the container must be lifted is given by,
[tex]v=\frac{d}{t}[/tex]Where t is the time it takes to lift the container at the calculated rate.
On substituting the known values,
[tex]\begin{gathered} 0.62=\frac{1}{t} \\ \Rightarrow t=\frac{1}{0.62} \\ =1.61\text{ s} \end{gathered}[/tex]Thus it takes 1.61 s to lift the container through 1 m at the given rate.
