One gram of fat contains 9 Calories, whereas each gram of protein and carbohydra

ID: 547964 • Letter: O

Question

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.

Alexander, who weighs 198 lb , decides to climb Mt. Krumpett, which is 5550 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

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

Explanation / Answer

Total energy required

mass = 198 lb = 0.454 * 198 = 89.892 kg

Ep = m*g*h = (89.892)(9.8)(5550) = 4889225.88 J

now..

Erequired = 4889225.88 J = 4889225.88/4.184 = 1168553.0 cal = 1168.5 Cal

from the bar:

1 bar = 10*9 + 40*4+50*4 = 450 Cal

then

n bars = (Erequired)/(E bar) = 1168.5 /450 = 2.59 = 3 bars required at least

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One gram of fat contains 9 Calories, whereas each gram of protein and carbohydra

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