Problem 97 - College Physics

Question

\(\bullet\) \(\bullet\) Energy requirements of the body. A 70 \(\mathrm{kg}\) human uses energy at the rate of \(80 \mathrm{J} / \mathrm{s},\) on average, for just resting and sleeping. When the person is engaged in more strenuous activities, the rate can be much higher. (a) If the individual did nothing but rest, how many food calories per day would she or he have to eat to make up for those used up? (b) In what forms is energy used when a person is resting or sleep- ing? In other words, what happens to those 80 \(\mathrm{J} / \mathrm{s} ?\) Hint: What kinds of energy, mechanical and otherwise, do our body components have?) (c) If an average person rested and did other low-level activity for 16 hours (which consumes 80 \(\mathrm{J} / \mathrm{s} )\) and did light activity on the job for 8 hours (which consumes \(200 \mathrm{J} / \mathrm{s} ),\) how many calories would she or he have to con- sume per day to make up for the energy used up?

Step-by-Step Solution

Answer

(a) ~1653 Cal/day for resting. (b) Energy is used in maintaining basic body functions. (c) ~2477 Cal/day for mixed activities.

Step 1: Calculate Energy Used for Resting in One Day

First, we need to calculate the total energy used when a person rests for a whole day. Since 1 day is equivalent to 24 hours, which is 86400 seconds, the energy consumed can be calculated by \( 80 \text{ J/s} \times 86400 \text{ seconds} = 6912000 \text{ J} \).

Step 2: Convert Joules to Calories

Convert the energy from joules to food calories, given that 1 food calorie (or kilocalorie) is equivalent to 4184 joules. Therefore, \( 6912000 \text{ J} \div 4184 \text{ J/cal} \approx 1652.87 \text{ Cal} \).

Step 3: Understand Forms of Energy Used

In rest or sleep, the body uses energy to maintain basic bodily functions such as breathing, maintaining body temperature, blood circulation, and cellular metabolism. These processes require minimal mechanical energy but are mainly focused on sustaining basic life processes with baseline biological energy.

Step 4: Calculate Energy for Mixed Activity in a Day

For 16 hours of resting, the energy consumption is \( 80 \text{ J/s} \times 16 \times 3600 \text{ seconds} = 4608000 \text{ J} \). For 8 hours of light activity with 200 J/s consumption, the energy used is \( 200 \text{ J/s} \times 8 \times 3600 \text{ seconds} = 5760000 \text{ J} \). Adding these gives a total daily energy usage of \( 10368000 \text{ J} \).

Step 5: Convert Total Energy to Calories for Mixed Activities

Convert \( 10368000 \text{ J} \) to food calories using \( 1 \text{ Cal} = 4184 \text{ J} \). Thus, the energy in calories is \( 10368000 \text{ J} \div 4184 \text{ J/cal} \approx 2477.23 \text{ Cal} \).

Key Concepts

Caloric Intake

Caloric intake refers to the total number of calories consumed through food and beverages in a day. These calories are what provide the energy needed for bodily functions and activities. On a day where an individual solely rests, approximately 1652.87 food calories are needed just to fuel the body's basic requirements such as breathing and maintaining warmth. This amount signifies the minimum energy intake necessary to sustain life without any additional physical activity.

Resting Energy Expenditure

Resting energy expenditure (REE) is the amount of energy, or calories, that a person uses at rest to maintain vital functions. These functions include breathing, circulating blood, and cellular metabolism. For a 70 kg human, this energy expenditure is about 80 joules per second when at rest or asleep. This expenditure translates to about 6912000 joules per day, or 1652.87 food calories, which are necessary just to maintain essential bodily processes without any additional movement.

Mechanical and Physiological Energy

When our bodies are at rest, they primarily use physiological energy to support processes like blood circulation, breathing, and maintaining body temperature. These processes consume minimal mechanical energy. The energy, comprising 80 joules per second at rest, is used to fuel the biological mechanisms that sustain life, rather than performing physical movement or external work.

Energy Conversion

Energy conversion is the process of changing energy from one form to another. In the human body, chemical energy from food is converted into other forms such as mechanical, thermal, and electrical energy. For example, when food is digested, the chemical energy is transformed into kinetic energy for movement or thermal energy to regulate body temperature. Thus, when at rest or engaged in light activities, this energy conversion ensures the body can perform necessary functions such as muscle contractions and maintaining warmth.

Physical Activity Energy Expenditure

Physical activity energy expenditure is the energy used during physical movement, including any exercise or day-to-day activities beyond basic resting functions. For instance, a person engaged in light activity uses 200 joules per second, translating to 5760000 joules in an 8-hour period. Combining this with energy used while resting will result in total energy usage of about 10368000 joules per day, or approximately 2477.23 food calories, demonstrating the increased energy requirements associated with movement compared to rest.