A 735 N person walks up three flights of stairs, covering a total vertical distance of 10.0 m. If, as is typical, only 20.0% of the caloric (food) energy is converted to work by the muscles, how many joules and food calories of energy did the person use? (One food calorie 4186 J.)
Five times the energy needed to climb the stairs. That would be 5 x 735 x 10 Joules.
Convert that to food calories using the conversion factor provided.
To calculate the energy used by the person, we need to consider the work done in walking up the stairs.
The work done is given by the formula:
Work = Force × Distance
Here, the force is the weight of the person, which is given as 735 N (Newtons), and the distance is 10.0 m (meters). So, substituting the values into the formula, we have:
Work = 735 N × 10.0 m
Now, let's calculate the work done:
Work = 735 N × 10.0 m
= 7350 N·m (Newton-meters) or Joules (J)
Now, we know that only 20% of the caloric energy is converted to work. To find the energy in food calories, we need to divide the work by the conversion factor of 4186 J/calories:
Energy (calories) = Work (J) / Conversion factor (J/calorie)
Energy (calories) = 7350 J / 4186 J/calorie
Calculating further:
Energy (calories) = 1.756 calories
To convert this value to food calories, we simply divide it by 1000:
Energy (food calories) = 1.756 calories / 1000
Energy (food calories) = 0.001756 food calories
Therefore, the person used approximately 7350 Joules (J) of energy and 0.001756 food calories to walk up the stairs.