a 715 N person walks up three flights of stairs, covering a total vertical distance of 10.5 m. (a) If, as is typical, only 20% of the caloric (food) energy is converted to work by the muscles, how many joules and food calories of energy did the person use? (1 food calorie=4186J)

I will be happy to critique your work.

Thanks, I am unsure of how to start the problem though.

work=mass*g(height)

energy in= work/.2= ...

watch units.

To find the amount of energy used by the person, we need to calculate the work done against gravity as the person walks up the stairs.

The work done against gravity is given by the formula:

Work = Force × Distance × cos(θ),

where
- Force is the weight of the person (715 N),
- Distance is the total vertical distance covered (10.5 m),
- θ is the angle between the force and the direction of motion (0° for vertical motion, so cos(0) = 1).

Substituting the given values, we have:

Work = 715 N × 10.5 m × cos(0°) = 715 N × 10.5 m × 1,

Work = 715 N × 10.5 m = 7507.5 Joules.

Since only 20% of the caloric energy is converted to work by muscles, we can calculate the amount of energy needed to do that work. Multiply the work done by 1/(20/100) (since 20% is converted to work) to get the total energy used.

Energy Used = Work / (20/100) = 7507.5 J / 0.2,

Energy Used = 37537.5 J.

To convert the energy used from joules to food calories, we can use the conversion factor of 1 food calorie = 4186 J.

Energy Used (in food calories) = Energy Used (in joules) / Conversion Factor,

Energy Used (in food calories) = 37537.5 J / 4186 J/cal,

Energy Used (in food calories) ≈ 8.96 calories.

Therefore, the person used approximately 37537.5 joules and 8.96 food calories of energy.