± Nutritional Energy One gram of fat contains 9 Calories, whereas each gram of p

Question

± Nutritional Energy

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

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.

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± Nutritional Energy

Alexander, who weighs 189 lb , decides to climb Mt. Krumpett, which is 5560 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?

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

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bars

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Explanation / Answer

m = 189 lb, h = 5560 m;

Energy of bars = (10*9 + 40*4 + 50*4) = 450 Cal/g = 450*4.184 kJ/g = 1882.8 kJ/g

now, calcualte Energy required to go to the top.

E = m*g*h

m = 189*0.454 = 85.729 kg

E = (85.729)(9.8)(5560) = 4671201.752 J

E = 4671201.752 J = 4671.2 kJ

Etotal = Eup + Edown = 4671.2 + 4671.2 = 9342.4 kJ

Then

bars required = (Etota)/( Ebar) = 9342.4 / 1882.8 = 4.96

nearest number will be 5 bars required

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