Alexander, who weighs 159 lb , decides to climb Mt. Krumpett, which is 5580 m hi

Question

Alexander, who weighs 159 lb , decides to climb Mt. Krumpett, which is 5580 m high. For his food supply, he decides to take nutrition bars. The label on the bars states that each 100-g bar contains 10g of fat, 40 g of protein, and 50 g of carbohydrates.

One gram of fat contains 9 Calories, whereas each gram of protein and carbohydrates contains 4 Calories.

Nutrition facts

Calories per gram

Fat

9

Protein

4

Carbohydrates

4

Part A

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?

Enter the exact answer to two significant figures. Do not round to an integer.

Nutrition facts

Calories per gram

Fat

9

Protein

4

Carbohydrates

4

Explanation / Answer

E=mgh

First convert the weight to kg.

159 lb is 72.12 kg on earth.

E=(72.12 kg)(9.81m/s/s)(5580 m) = 3947834.376 Joules.

Times 2 for the way down = 7895668.752 Joules

We need to convert to Calories

7895668.752   Joules is 1.89 X10^3 kcal.



Then you need to calculate the amount of energy per bar.
Protein and carbs are 4kcal per gram, fat is 9kcal per gram

10g * 9kcal/g +40g * 4kcal/g + 50g * 4kcal/g = 450 kcal per bar.


That works out to 1.90 X10^3 kcal/ 450kcal = 4.2 bars.

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