Alexander, who weighs 159lbs , decides to climb Mt. Krumpett, which is 5460ft high. For his food supply, he decides to take nutrition bars. The label on the bars states that each 100g bar contains 10g of fat, 40g of protein, and 50g of carbohydrates.Alexander wants to know exactly how many bars to pack in his backpack for the journey. To provide a margin of safety, he assumes that he will need as much energy for the return trip as for the uphill climb. How many bars should Alexander pack?
How would I even go about solving this problem? The total calories is 450 for a total bar that I calculated, is this right?
I am getting 22.6, but it says that is the wrong answer.
450*2000*4.18=3762000
159*5460*9.8=8507772
I am setting them equal to eachother and getting 2.26, but it says the answer is wrong. Please help.
The energy needed to overcome gravity is
Eg = mgy
m = (159 lbs)(2.20kg/lb) = 72.3kg
g = 9.8 N/kg
y = (5460ft)(12in/ft)(0.02536m/in) = 1662m
Substituting into the formula, you get the energy needed to climb to the top in joules.
Dividing joules by 4.18 gives you calories.
Dividing calories by 1000 gives you kilocalories, kcal.
1 kcal = 1 food calorie.
Look up the calorie equivalents for 1 gram of carbohydrate, 1g of fat, and 1 g protein. Use them to get the calorie value of each nutrition bar. This should give you a start.
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GK, you're very first calculation is incorrect. You divided 159 by 2.2. If there are 2.2 kg PER pound, you would multiply the pounds by the factor conversion to kg.
To solve this problem, you need to calculate the total energy required for Alexander's climb and compare it to the total energy provided by the nutrition bars.
First, let's calculate the total energy required for the climb. We can do this by multiplying Alexander's weight (159 lbs) by the height of Mt. Krumpett (5460 ft) and the acceleration due to gravity (9.8 m/s^2).
However, we need to convert Alexander's weight from pounds to kilograms and the height of the mountain from feet to meters for the formula to work properly.
1 pound = 0.45359237 kilograms
1 foot = 0.3048 meters
Weight on Mt. Krumpett = 159 lbs * 0.45359237 kg/lb = 72.12110783 kg
Height of Mt. Krumpett = 5460 ft * 0.3048 m/ft = 1664.6872 m
Energy required for the climb = Weight on Mt. Krumpett * Height of Mt. Krumpett * Acceleration due to gravity
Now, let's calculate the total energy provided by the nutrition bars. Each 100g bar contains 10g of fat, 40g of protein, and 50g of carbohydrates. To calculate the energy content of each bar, we need to know the energy per gram for each macronutrient.
Fat: 1 gram of fat provides 9 calories
Protein: 1 gram of protein provides 4 calories
Carbohydrates: 1 gram of carbohydrates provides 4 calories
Energy per bar = (10g * 9 calories/g) + (40g * 4 calories/g) + (50g * 4 calories/g)
Now, divide the total energy required for the climb by the energy provided per bar to find out how many bars Alexander should pack.
Number of bars = Total energy required for the climb / Energy per bar
Let's calculate each step:
Weight on Mt. Krumpett = 72.12110783 kg
Height of Mt. Krumpett = 1664.6872 m
Acceleration due to gravity = 9.8 m/s^2
Energy required for the climb = Weight on Mt. Krumpett * Height of Mt. Krumpett * Acceleration due to gravity
Energy required for the climb = 72.12110783 kg * 1664.6872 m * 9.8 m/s^2
Energy required for the climb = 850.7772101558925 kJ (approx)
Energy per bar = (10g * 9 calories/g) + (40g * 4 calories/g) + (50g * 4 calories/g)
Energy per bar = 450 calories (approx)
Number of bars = Energy required for the climb / Energy per bar
Number of bars = 850.7772101558925 kJ / 450 calories
Number of bars = 1.8903838003462 (approx)
Therefore, Alexander should pack at least 2 nutrition bars to provide enough energy for the climb and the return trip, assuming each bar provides 450 calories.