Alexander, who weighs 201 lb , decides to climb Mt. Krumpett, which is 5700 m hi

Question

Alexander, who weighs 201 lb , decides to climb Mt. Krumpett, which is 5700 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 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?

Explanation / Answer

Mass of Alexander = 201 lb x 1kg/(2.20462 lb)

= 91.2 kg

Work done by Alexander = force x distance

= mass x g x height

= 91.2 kg x 9.81 m/s2 x 5700 m

= 5099630.4 J x 1kJ/1000 J

= 5099.63 kJ

Calories required = 5099.63 kJ x 1kcal/4.184kJ

= 1218.84 kcal

For the return trip and uphill climbing

Total Calories required = 2 x 1218.84 = 2437.68 kcal

1 Calories = 1 kcal

kcal per bar = (9kcal/gfat x 10gfat) + (4kcal/gprotein x 40g protein) + (4kcal/gcarb x 50gcarb)

= 90 + 160 + 200

= 450 kcal

Number of bars required = 2437.68 kcal / 450 kcal

= 5.42

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