An 80 kg hiker climbs a 1000 m high hill at a constant speed. If the hiker's body is 25% efficient, how many kg of fat does the hiker burn in climbing the hill? Given: heat of reaction of body fat is 37000 kilo joules per kilogram.
I know that change in potential energy is 800,000. I just don't know what to do next.
m g h = increase of potential energy
80 * 9.81 * 10^3 = 785*10^3 Joules
785*10^3 = (1/4) total fuel energy burned
so
total fuel burned = 3.14 * 10^6 Joules
3.14 * 10^6 J / 37*10^6 J/kg = .085 kg
To calculate the amount of fat the hiker burns, we need to first calculate the total energy the hiker expended while climbing the hill. We can then use the hiker's efficiency to determine the amount of energy from fat burned.
The potential energy change can be calculated using the formula:
Potential energy change = mass * gravity * height
Given:
Mass of hiker (m) = 80 kg
Height of hill (h) = 1000 m
Gravity (g) = 9.8 m/s^2
Potential energy change = 80 kg * 9.8 m/s^2 * 1000 m = 784,000 J
Since the hiker's body is only 25% efficient, we need to calculate the total energy expended by dividing the potential energy change by the efficiency:
Total energy expended = Potential energy change / Efficiency
Total energy expended = 784,000 J / 0.25 = 3,136,000 J
Now, to determine the amount of fat burned, we need to convert the total energy expended into kilograms of fat. Given the heat of reaction of body fat is 37,000 kJ/kg, we need to convert the total energy expended from joules to kilojoules:
Total energy expended = 3,136,000 J / 1000 = 3136 kJ
The amount of fat burned can be calculated by dividing the total energy expended by the heat of reaction of body fat:
Amount of fat burned = Total energy expended / Heat of reaction of body fat
Amount of fat burned = 3136 kJ / 37,000 kJ/kg
Calculating this division, we find:
Amount of fat burned ≈ 0.08459 kg (rounded to 5 decimal places)
Therefore, the hiker would burn approximately 0.08459 kg of fat while climbing the hill.