A standard man climbs 10 m up a vertical rope. How much energy in calories is dissipated as heat in a single climb if 20% of the total energy required is used to do the work?
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To calculate the energy dissipated as heat in a single climb, we first need to determine the total energy required for the climb, and then calculate 20% of that total energy.
The energy required to perform work is given by the formula:
Energy = work done + energy dissipated as heat
Given that 20% of the total energy required is used to do the work, we can express the equation as:
Total Energy = Work Done + 0.2 * Total Energy
Since we know that the man climbs 10 m, we can calculate the work done using the formula:
Work Done = force × distance
Typically, when climbing a vertical rope, we assume that the only force acting is gravity, and its value is equal to the weight of the man.
So, the work done can be calculated as:
Work Done = weight × distance
The weight of a person can be approximated as the mass multiplied by the acceleration due to gravity (9.8 m/s^2).
Now, to calculate the total energy required:
Total Energy = Work Done + Energy Dissipated as Heat
Using the formula above, we can rearrange it to solve for the Energy Dissipated as Heat:
Energy Dissipated as Heat = Total Energy - Work Done
Let's plug in the values and calculate step-by-step:
1. Calculate the weight of the person:
Weight = mass × acceleration due to gravity = (mass) × 9.8 m/s^2
2. Calculate the work done:
Work Done = weight × distance
3. Calculate the total energy required:
Total Energy = Work Done / (1 - 20%)
4. Calculate the energy dissipated as heat:
Energy Dissipated as Heat = Total Energy - Work Done
By following these steps and substituting the values for mass (standard value for a man), distance (10 m), and the percentage of energy used for work (20%), you can find the amount of energy dissipated as heat in a single climb in calories.