Final answer:
The person's useful power output while shoveling snow, given an 800 W metabolism rate and 25% efficiency, is 200 W. She will take 176.4 seconds to lift 3000 kg of snow 1.20 m based on that power output, generating 105.84 kJ of waste heat in the process. Option c is the correct answer.
Step-by-step explanation:
Shoveling snow is an activity that demonstrates the principles of work, power, and energy in physics, particularly when considering human efficiency in physical tasks. Here, we are tasked with answering several questions based on a scenario where a person is shoveling snow. Let's break down each part of the question.
(a) What is her useful power output?
Given that the person metabolizes food at an 800 W rate, we must consider the efficiency of the human body when performing tasks like shoveling snow. Human muscle efficiency is typically around 25% when converting metabolic energy to mechanical energy. Therefore, the useful power output is:
800 W × 0.25 = 200 W
The correct option for her useful power output is None of the provided choices (A. 600 W; B. 700 W; C. 800 W; D. 900 W) are correct.
(b) How long will it take her to lift 3000 kg of snow 1.20 m?
The work done can be calculated as the product of force (weight of the snow) and the distance (vertical height). The formula for work (W) is:
W = m × g × h
W = 3000 kg × 9.8 m/s² × 1.20 m = 35280 J
The time (t) to lift the snow can be found using the formula:
t = W / Power
t = 35280 J / 200 W = 176.4 seconds
(c) How much waste heat transfer in kilojoules will she generate in the process?
The waste heat produced is the difference between the total energy expended and the useful work done. The total energy can be found by multiplying the metabolic power rate by time. The useful work is 35280 J (as calculated above). Since 75% of the energy is wasted (100% - 25% efficiency), the heat transfer can be calculated as:
Heat = (Metabolic power rate × time × 0.75)
Heat = (800 W × 176.4 s × 0.75) / 1000 = 105.84 kJ
The woman generates 105.84 kJ of waste heat in the process.