The label on a candy bar says 410 Calories.Assuming a typical efficiency for energy use by the body, if a 74kg person were to use the energy in this candy bar to climb stairs, how high could she go?
Convert the Calories (kcal) to Joules, then set equal to work (mg*height)
1.72E6joules=74*9.8*height
A high walk.
To determine how high the person could climb using the energy from the candy bar, we need to know the efficiency of energy conversion from food to mechanical work. Typically, the human body is estimated to have an efficiency of around 20-25% in converting food energy to mechanical work.
To calculate the amount of energy that can be obtained from the candy bar, we need to convert the 410 Calories into joules since joules are the standard unit of energy.
1 Calorie is equal to 4.184 joules. Therefore, 410 Calories can be converted to joules by multiplying it by the conversion factor:
410 Calories * 4.184 joules/Calorie = 1715.04 joules
Now, let's assume a typical 20% efficiency for energy conversion. Multiply the 1715.04 joules by the efficiency factor:
1715.04 joules * 0.20 = 343.008 joules
Next, we need to convert the energy in joules to potential energy (PE) in climbing stairs. The potential energy of an object near the Earth's surface can be calculated using the equation:
PE = m * g * h
Where:
PE is the potential energy,
m is the mass of the person (74 kg),
g is the acceleration due to gravity (9.8 m/s^2),
and h is the height reached.
Rearranging the equation, we can solve for h:
h = PE / (m * g)
Substituting the known values:
h = 343.008 joules / (74 kg * 9.8 m/s^2) ≈ 0.472 meters
Therefore, the person could theoretically climb approximately 0.472 meters using the energy from the candy bar, assuming a 20% efficiency.