Question

A typical human brain has a mass of 1.4 kg, which makes up about 2% of a person's mass. However, the brain requirs 20% of the body's power consumption. In essence, the brain requires 10 times as much power as any other organ in the body. The average power output of the human brain is about 2.0 x 10^1 W. Assume that the brain's power output could be converted into mechanical work and calculate how high we could use this power to lift an apple (m=0.20 kg) in one minute

Answer 1

To determine how high we could lift an apple using the power output of the human brain, we follow these steps:

 1. Calculate the work done by the brain's power output in one minute: Given: Power output of the brain = 20 W Time = 60 seconds  Work = Power x Time Work = 20 W x 60 s Work = 1200 J (joules)

2. Find the height the apple could be lifted using this work: Given: Mass of the apple (m) = 0.20 kg Acceleration due to gravity (g) = 9.81 m/s^2  

Work = Force x Distance Force = Weight of the apple = m x g Distance = Height (h)  Work = m x g x h h = Work / (m x g) h = 1200 J / (0.20 kg x 9.81 m/s^2) h = 1200 J / 1.962 N h ≈ 611.30 meters  

Therefore, the power output of the human brain could lift an apple to a height of approximately 611.30 meters in one minute.

Answer 2

Answer:

$612.24m \, \textsf{m}$

Explanation:

To calculate the height to which the brain's power output could lift an apple in one minute, we can use the concept of mechanical work and energy conservation.

First, let's determine the work done by the brain in lifting the apple. The work done in lifting an object against gravity is given by the formula:

$\textsf{Work} = \textsf{Force} \times \textsf{Distance}$

The force required to lift the apple against gravity is equal to its weight, which is given by:

$F = m \times g$,

where

• $m$ is the mass of the apple and
• $g$ is the acceleration due to gravity (approximately $9.8 \, \textsf{m/s}^2$).

Given:

• Mass of the apple, $m = 0.20 \, \textsf{kg}$
• Acceleration due to gravity, $g = 9.8 \, \textsf{m/s}^2$

The force required to lift the apple is:

$F = 0.20 \, \textsf{kg} \times 9.8 \, \textsf{m/s}^2 = 1.96 \, \textsf{N}$

Now, let's determine the work done by the brain in one minute, which is equal to the power output of the brain multiplied by the time duration. We'll need to convert one minute into seconds:

$\textsf{Time} = 1 \, \textsf{minute} = 60 \, \textsf{seconds}$

Given:

• Power output of the brain, $P = 2.0 \times 10^1 \, \textsf{W}$
• Time, $t = 60 \, \textsf{s}$

The work done by the brain in one minute is:

$\textsf{Work} = P \times t = (2.0 \times 10^1 \, \textsf{W}) \times (60 \, \textsf{s}) = 1.2 \times 10^3 \, \textsf{J}$

Now, we can find the distance (height) over which the work is done using the work-energy principle. The work done by the brain is converted into gravitational potential energy, given by:

$\textsf{Work} = \textsf{Change in potential energy}$

$\textsf{Work} = mgh$

Where:

• $m$ is the mass of the apple
• $g$ is the acceleration due to gravity
• $h$ is the height over which the apple is lifted

We know the work done (1.2 x 10^3 J) and the mass of the apple (0.20 kg), and $g = 9.8 \, \textsf{m/s}^2$. We can rearrange the equation to solve for $h$:

$h = \dfrac{\textsf{Work}}{mg}$

$h = \dfrac{1.2 \times 10^3 \, \textsf{J}}{0.20 \, \textsf{kg} \times 9.8 \, \textsf{m/s}^2}$

$h = \dfrac{1.2 \times 10^3}{1.96}$

$h = 612.244898 \, \textsf{m}$

$h = 612.24 \, \textsf{m ( in nearest tenth)}$

So, the height to which the brain's power output could lift an apple in one minute is approximately $612.24m \, \textsf{m}$.