Question

The average power output of the human heart is \(1.33 \mathrm{~W}\). (a) How much energy does the heart produce in a day? (b) Compare the energy found in part (a) with the energy required to walk up a flight of stairs. Estimate the height a person could attain on a set of stairs using nothing more than the daily energy produced by the heart.

Short answer

In a day, the heart produces 114912 J. This energy can lift a 70 kg person about 167.45 meters up in stairs.

Step-by-step solution

Calculate Energy Produced in a Day

To determine the total energy produced in a day by the heart, we use the formula for energy, which is the product of power and time: \( E = P \times t \). The power \( P \) is given as \( 1.33 \mathrm{~W} \) and the time \( t \) is 24 hours or \( 24 \times 3600 = 86400 \) seconds in a day. Hence, the energy is: \( E = 1.33 \times 86400 = 114912 \mathrm{~J} \).

Compare with Energy to Walk up Stairs

The typical energy required to walk up a flight of stairs depends on the height of the stairs and the person's weight. Assuming a 70 kg person, the energy required to climb a height \( h \) is given by \( E_{stairs} = m \times g \times h \), where \( m = 70 \mathrm{~kg} \) and \( g = 9.8 \mathrm{~m/s^2} \). We set the energy produced in a day equal to the energy to walk up \( h \) meters: \( 114912 = 70 \times 9.8 \times h \).

Solve for Height

Rearrange the equation from Step 2 to solve for \( h \): \( h = \frac{114912}{70 \times 9.8} = 167.448 \mathrm{~m} \). Thus, the energy produced by the heart in one day can lift a 70 kg person approximately 167.45 meters.

Key concepts

Power and Energy

In physics, energy is the capacity to perform work, and power is the rate at which work is performed or energy is transferred. Power and energy are thus closely related concepts. Understanding this relationship requires knowing that power is the amount of energy consumed or produced per unit of time.

To illustrate, if the human heart generates a power output of 1.33 watts, it converts energy at a rate of 1.33 joules per second. Over a day, the heart produces a substantial amount of energy, calculated by multiplying power by time. As calculated, the heart produces about 114,912 joules in a day. Think of this as the heart keeping you "powered" for 24 hours without any rest!

• Power is measured in watts (W), where 1 W = 1 joule/second.
• Energy is measured in joules (J).
• The formula connecting them is: Energy = Power × Time.

Work and Power

Work and power are core concepts that help to understand how energy gets utilized in physical tasks. Work is done when a force causes an object to move, and power is how quickly this work is performed.

In our heart example, the energy used by the heart over a day is the work done to sustain life functions. Now, if you compare this work to walking up stairs, it's easier to imagine how much energy is involved in everyday activities. Walking up stairs requires energy to lift your body weight against gravity.

• Work = Force × Distance
• Power = Work ÷ Time
• Force includes gravity, which is modelled by your weight (mass × gravity).

While the heart works continuously, other activities are intermittent but require focused bursts of energy.

Energy Conversion

Energy conversion is the process of changing one form of energy to another. In everyday life, our bodies convert the chemical energy from food into mechanical energy for movement and heat energy to maintain body temperature.

In the context of walking up stairs, the energy output of the heart could theoretically be used to lift a person. Even though this conversion doesn't happen directly, it illustrates how much potential energy you have stored from your heart's continuous work. For a 70 kg person, this energy allows them to reach up to 167.45 meters in height when walking up stairs purely from the heart's daily energy output.

• Energy conversion is key in technologies like engines and batteries.
• Potential energy relates to an object's position, such as height.
• Knowing how to calculate potential energy is crucial; it’s given by: Potential Energy = Mass × Gravity × Height.

By understanding energy conversion, you can better appreciate how the heart's energy supports everything from basic metabolism to ambitious physical activities.