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Ch 09: Work and Kinetic Energy
Knight Calc - Physics for Scientists and Engineers 5th Edition
Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796Non è quello che usi tu?Cambia libro di testo
Tutti i libri di testoKnight Calc 5th EditionCh 09: Work and Kinetic EnergyProblema 62c
Capitolo 9, Problema 62c

When you ride a bicycle at constant speed, nearly all the energy you expend goes into the work you do against the drag force of the air. Model a cyclist as having cross-section area 0.45 m² and, because the human body is not aerodynamically shaped, a drag coefficient of 0.90. Use 1.2 kg/m³ as the density of air at room temperature. The food calorie is equivalent to 4190 J. How many calories does the cyclist burn if he rides over level ground at 7.3 m/s for 1 h?

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Step 1: Start by calculating the drag force experienced by the cyclist using the drag force formula: \( F_d = \frac{1}{2} C_d \rho A v^2 \), where \( C_d \) is the drag coefficient, \( \rho \) is the air density, \( A \) is the cross-sectional area, and \( v \) is the velocity of the cyclist.
Step 2: Substitute the given values into the drag force formula: \( C_d = 0.90 \), \( \rho = 1.2 \ \text{kg/m}^3 \), \( A = 0.45 \ \text{m}^2 \), and \( v = 7.3 \ \text{m/s} \). This will give you the drag force \( F_d \).
Step 3: Calculate the power required to overcome the drag force using the formula: \( P = F_d \cdot v \), where \( F_d \) is the drag force and \( v \) is the velocity of the cyclist.
Step 4: Determine the total energy expended by the cyclist over 1 hour by multiplying the power \( P \) by the time \( t \) in seconds. Since 1 hour is 3600 seconds, the total energy is \( E = P \cdot t \).
Step 5: Convert the total energy from joules to food calories using the conversion factor: \( 1 \ \text{food calorie} = 4190 \ \text{J} \). Divide the total energy \( E \) by 4190 to find the number of calories burned by the cyclist.

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Drag Force

The drag force is the resistance experienced by an object moving through a fluid, such as air. It is influenced by the object's speed, cross-sectional area, and drag coefficient. The formula for drag force (F_d) is F_d = 0.5 * C_d * A * ρ * v², where C_d is the drag coefficient, A is the cross-sectional area, ρ is the fluid density, and v is the velocity. Understanding drag force is crucial for calculating the energy required to overcome it while cycling.
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Intro to Centripetal Forces

Work and Energy

Work is defined as the energy transferred when a force is applied over a distance. In the context of cycling, the work done against drag force translates into energy expenditure. The relationship between work (W), force (F), and distance (d) is given by W = F * d. This concept is essential for determining how much energy the cyclist uses to maintain a constant speed against the drag force over a specific distance.
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The Work-Energy Theorem

Caloric Energy Conversion

Caloric energy conversion refers to the process of converting energy expenditure into food calories. One food calorie is equivalent to 4190 joules. To find out how many calories a cyclist burns, one must calculate the total work done against drag force and then convert that energy from joules to calories using the conversion factor. This concept is vital for understanding the relationship between physical activity and energy consumption.
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