How many grams of carbohydrate does a person of mass 75 kg need to metabolize to climb five flights of stairs (15 m height increase)? Each gram of carbohydrate provides 17.6 kJ of energy. Assume 10.0% efficiency—that is, 10.0% of the available chemical energy in the carbohydrate is converted to mechanical energy.
g
What happens to the other 90% of the energy?
Could someone show me how to do this please. Thanks. I have a hard time figuring it out.
physics - Count Iblis, Friday, June 8, 2012 at 2:07pm
The person needs to do an amount of work of W = 75 kg * 15 m * 9.81 m/s^2 against gravity.
Per gram of carbohydrates, you have available 10% of 17.6 KJ to do mechanical work, so you need to divide W by 1.76 KJ to find the amount of carbohydrates needed in grams.
The other 90% converted to heat.
part a i tried it and it gave me 11036.25 that was wrong i put 110.36 that was wrong so i don't know how to do it and the answer has to be in g???please help. Thank you
No one has answered this question yet.
PE=m•g•h=75•9.81•15=11036 J.
11036 J is 10% ,
x is 100%
x=110360 J.
110360/17600=6.27 g
To calculate the amount of carbohydrates needed to metabolize and climb the five flights of stairs, we need to follow these steps:
1. Calculate the work done against gravity:
The work done against gravity is given by the formula: W = mgh
Where:
m = mass of the person (75 kg)
g = acceleration due to gravity (approx. 9.81 m/s^2)
h = height increase (15 m)
Substituting the values, we have: W = 75 kg * 15 m * 9.81 m/s^2 = 11036.25 J (Joules)
2. Convert the work done into kilojoules (kJ):
Since 1 kJ = 1000 J, the work done is equal to 11.03625 kJ.
3. Calculate the amount of carbohydrates needed in grams:
Each gram of carbohydrate provides 17.6 kJ of energy, with 10% efficiency.
Therefore, the amount of carbohydrates needed can be calculated by dividing the work done (in kJ) by the energy provided by one gram of carbohydrate (17.6 kJ), and then dividing by the efficiency (10% or 0.1):
Carbohydrates needed = (11.03625 kJ / 17.6 kJ) / 0.1 = 62.75 g
So, a person with a mass of 75 kg would need to metabolize approximately 62.75 grams of carbohydrates to climb five flights of stairs with a 15 m height increase.
Regarding the question about the remaining 90% of energy, it is converted to heat. This is due to the inefficiency of converting chemical energy into mechanical energy, with some energy being lost as heat during the metabolism process.