To determine the energy used by a person weighing 75 kg while climbing four flights of stairs, we first need to calculate the gravitational potential energy gained during the climb. This energy can then be adjusted for the efficiency of the muscle system and converted into dietary calories.
Calculating Gravitational Potential Energy
The formula for gravitational potential energy (PE) is:
PE = m × g × h
- m = mass (in kg)
- g = acceleration due to gravity (approximately 9.81 m/s²)
- h = height (in meters)
For our scenario:
- m = 75 kg
- g = 9.81 m/s²
- h = 15 m
Plugging in these values:
PE = 75 kg × 9.81 m/s² × 15 m
Calculating this gives:
PE = 75 × 9.81 × 15 = 1108.75 Joules
Adjusting for Muscle Efficiency
Since the muscle system is only 25% efficient, we need to account for this efficiency when calculating the total energy expenditure:
Energy Used = PE / Efficiency
Substituting the values:
Energy Used = 1108.75 Joules / 0.25
This results in:
Energy Used = 4435 Joules
Converting Joules to Dietary Calories
To convert the energy used into dietary calories, we use the conversion factor where 1 dietary calorie equals 4186 Joules:
Calories = Energy Used / 4186
Substituting the energy used:
Calories = 4435 Joules / 4186
This calculation yields:
Calories ≈ 1.06 dietary calories
Summary of Findings
In summary, a person weighing 75 kg climbing four flights of stairs to a height of 15 meters would expend approximately 4435 Joules of energy, which is equivalent to about 1.06 dietary calories. This illustrates not only the energy demands of physical activity but also the importance of understanding efficiency in energy conversion within the human body.
