Question

Alexander, who weighs 162 lb , decides to climb Mt. Krumpett, which is 5350 m high. For his food supply, he decides to take nutrition bars. The label on the bars states that each 100-g bar contains 10 g 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 9g, Protein 4g, Carbohydrates 4g.

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?

Answer 1

we know that

E = mgh

Although you should convert the weight to kg.

162 lb is 73.48 kg on earth.

E=(73.48kg)*(9.81m/s^2)*(5350m) = 3856487.58 Joules.

Times 2 for the way down = 7712975.16 Joules

We need to convert to Calories

7712975.16 Joules is 1843.44 kcal.

Then we 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 1843.44 kcal/ 450kcal or 4.09 bars.