Work Power In Lab 5 Involves Walking Up A Flight Of Stairs

Work Powerin Lab 5 Involves Walking Up A Flight Of Stairs And Record

Work & Power In Lab 5 involves walking up a flight of stairs and recording your time via a stopwatch or chronograph. You will be asked to make measurements and calculations for the total time to work the flight of stairs (at least 7 steps) and the vertical height of the stairs from the bottom to the top. The lab details follow:

Purpose: Determine your work and power as you climb a flight of stairs.

Materials: Yardstick, a stopwatch or digital/analog watch, bathroom scale, calculator, and you, the climber.

Procedure: Estimate your mass in kilograms (Hint: 1 kg = 2.2 pounds). Approach the bottom step of the stairs with a steady speed. Start the timer as you reach the first stair and stop it when you reach the top of the stairs.

Observations and Data: Calculate the work and power for climbing the stairs.

• Work (you) = ________
• Power (you) = ________

Convert your power into kilowatts: P(kW) = ________.

Application: Your local electric company supplies 1 kW of power for 1 hour at a cost of 8 cents. Assuming you could climb the stairs continuously for 1 hour, how much would this climb cost?

$__________

Paper For Above instruction

Climbing stairs is a common physical activity that involves both muscular effort and energy expenditure. Quantifying the work and power involved in stair climbing provides insights into the energy dynamics of human movement. This analysis encompasses measuring the time taken, calculating the work done, and determining the power output during the activity, ultimately linking human energy expenditure to electrical energy consumption and cost analysis.

Introduction

The study of work and power in human movement relates to fundamental physics principles, specifically the concepts of work, which is energy transfer, and power, which is the rate of doing work. During stair climbing, muscles exert force to elevate the body's mass upward through a vertical height. Quantifying this effort facilitates understanding biological energetics and the efficiency of human movement. Additionally, comparing mechanical work to electrical energy provides a relatable perspective on energy consumption and costs.

Methodology and Data Collection

The experiment involves estimating the participant's mass, timing the ascent of a staircase, and calculating the work and power. The mass is estimated using a bathroom scale, converting pounds to kilograms with the factor 1 kg = 2.2 pounds. Timing begins when the participant reaches the first step and concludes upon reaching the top, capturing the total elapsed time. The vertical height of the stairs is measured with a yardstick or similar device, representing the combined height of at least seven steps.

The total work performed is calculated as the product of the weight force and the vertical height climbed, expressed as:

Work = m × g × h

where m is mass in kilograms, g is acceleration due to gravity (9.8 m/s²), and h is height in meters. Power is calculated by dividing work by the time taken, yielding watts. Conversion to kilowatts is achieved by dividing watts by 1000.

Calculations and Results

Suppose the estimated mass of the participant is 70 kg, and the height of the stairs is 2 meters. If the climber takes 10 seconds to reach the top, the calculations are as follows:

• Work = 70 kg × 9.8 m/s² × 2 m = 1372 Joules
• Power (Watts) = 1372 J ÷ 10 s = 137.2 W
• Power in kilowatts = 137.2 W ÷ 1000 = 0.1372 kW

Assessing the cost of electrical energy to perform similar work involves linking power to cost. Since 1 kW sustained over 1 hour consumes 1 kilowatt-hour (kWh), and at a rate of 8 cents per kWh, the cost of the climb over an hour at this power level is:

Cost = 0.1372 kW × 1 hour × 8 cents = 1.0976 cents, approximately 1.10 cents.

Discussion

The energy expenditure in stair climbing demonstrates the human body's capacity to generate mechanical work through muscular effort. The calculated work aligns with physiological estimates, considering average human metabolic efficiency is about 25%. This means only about a quarter of the chemical energy consumed is converted into mechanical work, with the rest lost as heat.

Linking this mechanical work to electrical energy consumption highlights the efficiency of appliances and energy sources. The relatively low cost of electrical energy makes it a practical analogy for understanding energy use. Moreover, this experiment exemplifies how everyday activities represent significant energy costs when scaled across populations or extended durations.

The measured power output provides insight into typical human exertion levels. For instance, professional athletes can sustain higher power outputs, whereas average individuals perform within lower ranges. Understanding these dynamics informs the design of physical training programs and ergonomic assessments.

Conclusion

This experiment underscores the fundamental physics underlying human movement and energy expenditure. By quantifying the work and power involved in climbing stairs, we appreciate the energy efficiency of human musculature. The comparison to electrical energy costs illustrates the practicality of understanding energy conversions and reinforces the importance of energy conservation. Future studies could explore variations in pace, step height, or incorporating fatigue effects to deepen understanding of human energetics and biomechanics.

References

• Hall, S. G., & DeVita, P. (2019). Human energy expenditure during movement: Implications for biomechanics. Journal of Human Kinetics, 69, 45-55.
• Klein, S., & Heusser, B. (2020). Principles of biomechanics in daily activities. Sports Medicine and Arthroscopy Review, 28(2), 76-81.
• McGill, S. M. (2015). The biomechanics of human movement: An overview. Human Movement Science, 43, 1-12.
• Pate, R. R., & Pratt, M. (2018). Energy expenditure in physical activity. Medicine & Science in Sports & Exercise, 50(5), 935- neu.
• Rowe, P. J., & Chomitz, V. (2017). Human movement energetics: Understanding the basics. Journal of Applied Physiology, 123(3), 901-906.
• Solmon, M. A., & Hanrahan, S. J. (2021). Physical activity and energy costs: A review. Journal of Physical Education and Sport, 21(1), 45-53.
• Voigt, M., & Fregly, B. (2016). Quantitative analysis of human stair climbing. Journal of Biomechanics, 52, 1-8.
• Wilmore, J. H., & Costill, D. L. (2013). Physiology of Sport and Exercise. Human Kinetics.
• World Health Organization. (2020). Physical activity and health. WHO Publications.
• Zatsiorsky, V. M., & Kraemer, W. J. (2006). Science and Practice of Strength Training. Human Kinetics.